No, the cities are not the same. One was earthly - the camp of the saints; and one is spiritual - the new Jerusalem.
Prophesy contains certain similes and metaphors that are defined from OT prophesy and scripture. Revelation is filled with OT prophesy and language of the destruction of Jerusalem.
The thousand years is not a literal period of time. It is symbolic for the fullness and completeness of God's appointed time.... when He deems the time to be right.
“Know therefore that the Lord thy God, he is God, the faithful God, which keepeth covenant and mercy with them that love him and keep his commandments to a thousand generations;” (Deu. 7:9, KJV)
“10 For every beast of the forest is mine, and the cattle upon a thousand hills.” (Psa. 50:10, KJV)
“For a day in thy courts is better than a thousand. I had rather be a doorkeeper in the house of my God, than to dwell in the tents of wickedness.” (Psa. 84:10, kJV)
“Be ye mindful always of his covenant; the word which he commanded to a thousand generations;” (1 Chron. 16:15, KJV)
Many try to make the comparison in 2 Pet. 3:8 of a thousand years as one day be literal. But they leave out the second part of the couplet, that a day is as a thousand years. They try to make it mean an amount of time, when the issue is the quality of time.
Excerpt from my post "A Thousand Years is AS One Day" (1):
“4 For a thousand years in thy sight are but as yesterday when it is past, and as a watch in the night.” (Psa. 90:4, KJV)
When we were children time seemed to pass very slowly because we were constantly waiting for something to happen, or waiting to be older so that we could do all the wonderful things our parents could do. As we get older, time seems to move faster. We never have enough of it to do everything we want to accomplish.
And as we grow very old, time moves so fast that our youth seems as yesterday.
“…and a thousand years as one day.”
We think that time moves slowly when we are in trouble, or enduring hardship. We ask “when”, “when will this end? When will this be over?” That is the question Peter was answering for those of the first century AD when this book was written – approx. 64-66 AD.
They were enduring great hardship, and much persecution under the tyranny from the Sanhedrin, and the Romans. They knew of the promise of Christ’s return to destroy the temple (Matt. ch. 24-25), and of His promised second appearance in that generation (Heb. 9:28). They were daily being accosted by scoffers (vs. 3) who were challenging what the apostles had told them, who were saying that all things continue the same (vs. 4).
It is very hard to keep on believing when people around you are constantly telling you that you are wrong. So, Peter was reassuring them that even though time in their perspective, as they measured it might seem to be moving slowly, that God was not slow to judge the wicked. His judgment was coming to them at the right time, the appointed time. (Note 6)
God’s judgments were always at God’s appointed times.
“5 And the Lord appointed a set time, saying, To morrow the Lord shall do this thing in the land.” (Ex. 9:5, KJV)
“15 So the Lord sent a pestilence upon Israel from the morning even to the time appointed: and there died of the people from Dan even to Beersheba seventy thousand men.” (2 Sam. 24:15, KJV)
“19 And he said, Behold, I will make thee know what shall be in the last end of the indignation: for at the time appointed the end shall be.” (Dan. 8:19, KJV)
So, when we read Revelation's thousand years we need to decode that prophetic symbol and replace it with God's definition ... His appointed time. Further from this same post:
The words “a thousand” are a metaphor God used in His prophesy for His perfectly completed and appointed time.
“And he laid hold on the dragon, that old serpent, which is the Devil, and Satan, and bound him a thousand years [the appointed time], 3 And cast him into the bottomless pit, and shut him up, and set a seal upon him, that he should deceive the nations no more, till the thousand years [the appointed time] should be fulfilled: and after that he must be loosed a little season. … and they lived and reigned with Christ a thousand years [the appointed time]. 5 But the rest of the dead lived not again until the thousand years [the appointed time] were finished. This is the first resurrection. … but they shall be priests of God and of Christ, and shall reign with him a thousand years [the appointed time]. 7 And when the thousand years [the appointed time] are expired, Satan shall be loosed out of his prison," (Rev. 20:2-7, KJV)
Heaven and Earth
Heaven and earth (God and Israel) is a compound metaphor for God's relationship / covenant with His people. In the OT under the Mosaic covenant, God's people were defined as the blood line of Abraham through Isaac.. the seed of promise. Under the gospel of Christ, the new covenant was spoken of as the new heaven and new earth, and it is the agreement / relationship with those of the line of faith (Rom. 9:7ff). It never meant that a literal new physical heaven and earth would replace the existing physical cosmos.
From my post "Frequent Mistakes - Part V: Roses Are Red, Violets Are Blue..." (2):
Couplets are very helpful in identifying and defining the symbols in God’s prophesies. The first part of the couplet will have either a synonym or antonym in the second part. Synonyms are usually indicated by the words “as” and “like.” Antonyms usually follow the word “but.”
Psa. 12:6, “The words of the Lord are pure words: as silver tried in a furnace of earth, purified seven times.” (KJV)
This poetic couplet compares God’s word to the purest of silver, purified seven times. The simile is indicated in the second half by the word “as”. The scripture does not mean that God’s words are literally silver.
Psa. 19: 1-2, “The heavens declare the glory of God; and the firmament sheweth his handywork. 2 Day unto day uttereth speech, and night unto night sheweth knowledge.” (KJV)
The Holy Spirit used anthropomorphism to attribute the ability of human speech to daylight, and personified the night as a teacher dispensing knowledge. Neither the day nor the night were literally speaking.
The literalists will agree with the most obvious of these spiritual comparisons, but then will insist that God’s word is always literal whenever they want the scriptures to support their personal interpretation of prophesy. They are not consistent in their application of “literal interpretation”. .......
We can keep looking for many more metaphors and similes throughout the scriptures, but there is one more in particular I have in mind. It is the couplet of Matt. 24:35.
“Heaven and earth shall pass away, but my words shall not pass away.” (KJV)
One thing would pass away, but another thing would not pass away. Just as in many other couplets of poetry and prophesy, the word “but” signals a comparison. When we examine this scripture closely we find that the comparison is between “Heaven and earth” and “my words”.
The word “but” indicates an antonym, something opposite to another. In this comparison, “heaven and earth” was opposed to, opposite of Christ’s words, “my words”. Then, “heaven and earth” must have been symbolic of someone else’s words, and was being used by Christ as an idiom. .....
Then, as Christ’s words (the gospel of the new covenant) would not pass away, and the disciples were to listen to Christ instead of to Moses, then Moses’ words were the ones passing away. In the prophetic couplet of Matt. 24:35, “Heaven and earth” was an idiom for the old Mosaic covenant.
When Isaiah prophesied of the new heaven and earth (Isa. 65:17-19) the context of the immediate fulfillment was of the rebuilding of Jerusalem after the return from the Babylonian captivity, and the reestablishment of the Mosaic covenant at the second temple.
The second and complete fulfillment of that prophesy was with the new spiritual Jerusalem that was created after the destruction of the earthly city (AD 70) when all of the saints under the gospel of Christ would be its inhabitants as described in Rev. 21. The new Jerusalem is the spiritual capital city of the new heaven and earth covenant under the gospel of Christ. It is not a physical place. (3)
God had destroyed that "beloved" city and its animal sacrificial temple through the agency of the Roman army in AD 70 because those animal sacrifices had become profane after Christ's sacrifice. God could not let that system continue since He had annulled it (Heb. 7:12-18).
That man has rebuilt another city on earth by that same name, and is attempting to rebuild a 3rd temple to reestablish the Mosaic covenant does not negate the fact that God finished and completed His promises under the gospel of Christ.
"21 Jesus saith unto her, Woman, believe me, the hour cometh, when ye shall neither in this mountain, nor yet at Jerusalem, worship the Father.
22 Ye worship ye know not what: we know what we worship: for salvation is of the Jews.
23 But the hour cometh, and now is, when the true worshippers shall worship the Father in spirit and in truth: for the Father seeketh such to worship him." (John 4:21-23, KJV)
The camp of the saints (Rev. 20:9) -
This is another reference to the earthly city of Jerusalem, the beloved city. We cannot jump from vs. 4 to vs. 9 in the scripture. Those who came up to surround the camp of the saints in vs. 9 were set for the destruction of the earthly city as stated in vs. 8. There is a great deal of OT prophesy that must be discussed to fully support this fulfillment of Daniel's prophesy, but this is the end of the days of the desolations of Jerusalem which Gabriel told Daniel all through Dan. 9 - 12. (4)
Fire from heaven is the metaphor of God's judgment. God's fury is fire (Lam. 2:4; Nah. 1:6). When used in prophesy "fire" should be replaced with "judgment". The heaven sent judgment that came upon those that dwellt in Jerusalem (the great city, the beloved city) was carried out by the Roman armies in AD 70 under Titus' legion whose standard was the lightning bolt ... fire from heaven. (5) (6) (7)
So, Rev. 20:9 depicts the destruction of the earthly city. Rev. 21:1-2 depicts the new heavenly spiritual Jerusalem in which the saints dwell with God. That it has come down to earth after the destruction of the earthly city in Rev. 20 (AD 70) does not mean it is a land based city.
All those in Christ are the temple (1 Cor. 3:16-17), and we dwell and tabernacle with God in His spiritual kingdom (Luke 17:20-21). God and the Lamb (Christ) are its light (Rev. 21:23). And without that city are the unbelievers and workers of iniquity (Rev. 22: 15).
As the unbelievers are living without (outside) that city, and the believers are in the city, then this is a representation of the spiritual state of man and our relationship with our heavenly Father. It is not speaking of a physical city where all believers on earth must live.
All believers of all of the nations of all of the earth flow into that spiritual city of God when they are clothed with Christ's righteousness, when they put on Christ (Rev. 22:14; Rev. 21:24; Mic. 4:2; Isa. 2:4).
Christ's everlasting kingdom was fully established after the destruction of that 2nd temple and that 2nd city of Jerusalem in AD 70. That marked the end of the old Mosaic covenant under which they lived in the 1st century AD, and which they called "this age". It marked the beginning of the new age, the one they called "the age to come," which is the Messianic age that all succeeding generations of those in Christ have enjoyed... the everlasting age of the everlasting kingdom of God which has no end (Eph. 3:21, Isa. 45:17).
There is much more that should be discussed but cannot be included here. All of the posts at my blog discuss the time of His coming, the prophesies of the destruction of Jerusalem, the reigning of the martyred saints in heaven, etc. Please see those listed in the notes and others at ShreddingTheVeil.
1) A Day Is AS A Thousand Years - ShreddingTheVeil
2) Frequent Mistakes - Part V: Roses Are Red, Violets Are Blue... here
3) The Signs of Revelation - Part VIII: The New Heavens And New Earth - here
4) Frequent Mistakes - Part III: The Last Day - here
5) The Gathering of The Elect - here
6) The Signs of Revelation - Part VI: Judgment Day, Chap. 20 - here
7) The Beast of Revelation - here