IDEA IN BRIEF
The relationship between the two visions is remarkable. That is, the "New Jerusalem" is the Zion above, which is the locus of the Kingdom or "Mount" of God in heaven. This heavenly Zion (New Jerusalem) will become the capital of the New Earth. This capital is not only the locus of the Presence of the Lord within heaven and earth, but also the dwelling place of all those who received eternal life through the New Covenant, and thus they, as citizens of the heavenly Jerusalem, are the "bride" of the Lord, who now live with Him on the New Earth.
When Moses was at Mount Sinai, he received the instructions for the tabernacle based on the "pattern" which had existed in heaven. That is, the earthly tabernacle (the facsimile) was the analog to the actual tabernacle in heaven (the original).
Exodus 25:9, 40 (NASB)
9 According to all that I am going to show you, as the pattern of the tabernacle and the pattern of all its furniture, just so you shall construct it.... 40 See that you make them after the pattern for them, which was shown to you on the mountain.
Number 8:4 (NASB)
4 Now this was the workmanship of the lampstand, hammered work of gold; from its base to its flowers it was hammered work; according to the pattern which the Lord had shown Moses, so he made the lampstand.
For example, inside the tabernacle there were pictures of cherubim swarming around the tabernacle. These cherubim were depicted on the interior veil covering of the tabernacle (Ex 26:1; Ex 26:31; Ex 36:8; Ex 36:35). In other words, these pictures of cherubim (depicted on the veil swarming around) had represented the real tabernacle in heaven, where real cherubim were swarming around the actual tabernacle. The Book of Hebrews summarizes this truth as follows:
Hebrews 8:4-5 (NASB)
4 Now if He were on earth, He would not be a priest at all, since there are those who offer the gifts according to the Law; 5 who serve a copy and shadow of the heavenly things, just as Moses was warned by God when he was about to erect the tabernacle; for, “See,” He says, “that you make all things according to the pattern which was shown you on the mountain.”
It was in this tabernacle in heaven (that was "not pitched by human hands" - Heb 8:2) in which Jesus had presented himself as both the priest and the sacrifice, by which the New Covenant came into effect (Heb 9:11-28), which replaced the Mosaic Covenant (Heb 8:6-12), which was just the facsimile, or "shadow" of what was in heaven (Heb 8:5).
Now this tabernacle in heaven was inside the heavenly Zion. That is, the Zion in heaven is the "mountain" or government of the God in heaven. Therefore, the Zion on earth was the analog of the government of God in heaven: The Jerusalem on earth therefore was the analog of the heavenly kingdom, which had become the theocratic kingdom of God on earth centered in Jerusalem. We see the Zion in heaven (or heavenly Jerusalem) in the two following passages... that is, we are able to see that there is the Kingdom of God in heaven, which is transposed over the earthly Jerusalem:
Isaiah 14:13 (NASB)
13 “But you said in your heart,
‘I will ascend to heaven;
I will raise my throne above the stars of God,
And I will sit on the mount of assembly
In the recesses of the north.
Psalm 48:1-2 (NASB)
1 Great is the Lord, and greatly to be praised,
In the city of our God, His holy mountain.
2 Beautiful in elevation, the joy of the whole earth,
Is Mount Zion in the far north,
The city of the great King.
The "in the...north" found in these two verses (בְּיַרְכְּתֵ יצָפֹון) and (יַרְכְּתֵי צָפֹון) is not some reference to some pagan land somewhere up north in the Fertile Crescent, but is in direct reference to what is above ("north") in heaven.
Therefore the holy mount in these passages refers to the Government of God ("mount" or "mountain") of Zion, which has been the locus of the Lord's kingdom in heaven. This locus also included the earthly Zion, where the physical tabernacle was "housed" in the temple in Jerusalem, which was an analog or facsimile of what was in heaven. The throne of the Lord's Government is in heaven (the original), but His Glory also dwelt in his temple on earth in Zion, which was the earthly Jerusalem (the copy). Please see Ps 11:4 and Ps 103:19.
So to tie the ideas together, the Zion in heaven is the Jerusalem above. The Old Covenant (Mosaic Law) was centralized in the Jerusalem on earth, where the tabernacle was "housed" in the temple. The big difference between the New Covenant and Old Covenant was not only the parallel between heaven and earth, but that the Mosaic Covenant "governs" affairs relating to mortal life (was therefore temporal) whereas the New Covenant "governs" affairs relating to immortal life (and therefore eternal).
In other words, in the Bible the term "Jerusalem" can refer either to the earthly "mother" or to the heavenly "mother": in the earth sense, her sons live mortal lives according to avoiding what is wrong (Law) - thus slavery to sin; in the heavenly sense, her sons live lives according to the Promise of eternal life, which end in immortality (Gal 4:21-30).
Galatians 4:26 (NASB)
26 But the Jerusalem above is free; she is our mother.
This "mother" is not only the locus of the Mountain of God (Zion), but is also the place where the tabernacle in heaven in located; that is, the locus of the New Covenant, which is the source of eternal life.
Hebrews 12:22-24 (NASB)
22 But you have come to Mount Zion and to the city of the living God, the heavenly Jerusalem, and to myriads of angels, 23 to the general assembly and church of the firstborn who are enrolled in heaven, and to God, the Judge of all, and to the spirits of the righteous made perfect, 24 and to Jesus, the mediator of a new covenant, and to the sprinkled blood, which speaks better than the blood of Abel.
The "firstborn" are those who have received eternal life at the Mount Zion of heaven. No one can be "born" if some life is not associated with "born"; in this case, being born from above, from heaven, refers to eternal life, which is the New Covenant.
In conclusion, the current heavens and current earth are temporary. Both will one day burn with intense fire (2 Pet 3:12-13), because both are "created things," which are to be removed.
Hebrews 12:25-28 (NASB)
25 See to it that you do not refuse Him who is speaking. For if those did not escape when they refused him who warned them on earth, much less will we escape who turn away from Him who warns from heaven. 26 And His voice shook the earth then, but now He has promised, saying, “Yet once more I will shake not only the earth, but also the heaven.” 27 This expression, “Yet once more,” denotes the removing of those things which can be shaken, as of created things, so that those things which cannot be shaken may remain. 28 Therefore, since we receive a kingdom which cannot be shaken, let us show gratitude, by which we may offer to God an acceptable service with reverence and awe;
The reason why the Jerusalem in heaven remains to become the New Jerusalem in the New Earth is because she is born, not created. (The verses in Hebrews, above, allude to the removal of those things created.) She is the bride, or as noted above, the general assembly of those who are "firstborn." What is also remarkable is that this New Jerusalem from heaven merges into the New Earth, and what was heavenly and what was earthly, now become indistinguishable. Thus, gold is "transparent" (Rev 21:18) and dimensions of space as understood by humans now become indistinguishable from those understood by angels (Rev 21:17).
In conclusion, the merging of the Zion from heaven to become the New Jerusalem of the New Earth is the consummation of the New Covenant, which provides eternal life (as a child is born from its mother). The New Jerusalem is the Government, or Mountain of God (Zion), which becomes not only the locus of the New Creation (merging human and angelic realms) but also the Presence of God (tabernacle of heaven now comes to earth) by whose glory the elect will dwell into eternity.