Yes, surely. Both are quotes of Isaiah 40:8: "The grass withers and the flowers fall, but the word of our God endures forever," and of Psalm 119(118):89 "Your word, o Lord, will last forever", and Psalm 33 (32):11 "The council of God remains forever, and thoughts of His heart from generation to generation" (ἡ δὲ βουλὴ τοῦ Κυρίου εἰς τὸν αἰῶνα μένει, λογισμοὶ τῆς καρδίας αὐτοῦ εἰς γενεὰν καὶ γενεάν.) Indeed, what has more dignity, the source, or that that, which comes out from the source? The first must be at least as dignified, if not more, than what comes out of it. Similarly, if word sourced out from Jesus remains forever, then necessarily to Jesus Himself, to the Source of this word, pertains divinity and eternity, which is clearly asserted of Him in the Gospels (cf. John 1:1 for His being God and eternal without reference to His Incarnation, or Paul in Hebrews 13:8, already with reference to the Logos's Incarnation - "Jesus Christ the same yesterday, and today, and for ever /εἰς τοὺς αἰῶνας/".)
No prophet or apostle would say this from his own person, for it would be a blasphemy; that's why they say that "Lord's word will remain forever", or "Your word, o Lord, will last forever"; on the contrary, Jesus says the same from His own Person, for He is the Lord God, whose word will remain forever.
As to the question concerning the Matthew 24:35: "Does "not pass away" mean for "all eternity", in contrast to "forever", meaning, "as long as this world exists?" - the "not pass away" in this passage means "eternally", "forever", because the "heaven and earth" stand for the entirety of creation, both visible and invisible, and only creation can end, whereas what is beyond creation, i.e. the word the Lord, is necessarily exempt from the category of ending, and thus possesses divine, supra-creaturly ever-ness.
However, if your question asks whether there is a twofold distinction in words of God, that is to say, a) one type of those words stand for those things that existed before the creation of the world and will not come to an end even if the world will be annihilated (such words can be like Father the Son and the Holy Ghost whispering to each other "I love Thee" in a divine language that has nothing to do with English and even with Homeric Greek); and b) another type of those words which stand for things that last only from the creation to the end of the universe. However, this distinction is not plausible at all, for even those words of God that relate to the concrete temporal facts in the history of mankind are eternal in Him and thus never pass away. It is, thus, eternal truth that "Abraham will become father of nations" (cf. Genesis 17:4) that was true before creation of the world, for God knew it even in that atemporal, prior-to-creational "then", and will be true and stand even after the consummation of the created universe, for it is still existing in God's eternal knowledge. Yet, the last possibility that the created world will be done away entirely so that there will remain again only the Trinity without created universe, is sheerly hypothetical, for the universe has a beginning, but not end, and one of the eternal uncreated hypostases of God, Logos, has adopted forever the human created nature, thus the preservation of the creation is guaranteed.
Again, to return to the gist of the matter, let us show that the Jesus' words have exactly the same divine dignity as the words attested to the Lord in Old Testament. In fact, what is more principal: a source, or that which comes out of source? Of course, the source, for it should contain at least as much as what comes out of it, and, moreover, it holds a causal and logical superiority. Now, if the Son, unlike servants, remains forever (John 8:35), then also all His essential features and attributes that are manifested from the eternal Son, the "word" being one of those attributes, also remain eternally, for how that what is essential to somebody who is eternal be not co-eternal?
Moreover, as to the servants, who are angels (Hebrews 1:14), they cannot speak out of their own sovereign authority, for they are just servants, and thus, nobody can pray to angels that they may commit this or that out of their sovereign authority; whereas Jesus can be asked to speak and act out of His sovereign authority, as God. That is why the wise centurion, understanding this, asks Him not to come to his house, but to "just say a word" and his servant would be healed (Matthew 8:8-9). That is to say, the centurion believed that Jesus had a self-sovereign authority over spirits (believed to be the causes of illnesses), just like he himself had authority over soldiers. Thus, Jesus' word is not for centurion an angelic word, but a self-sovereign divine word, for angels do not have self-sovereign authority over each other, so as to give orders and commands to each other. Even highest of angels, like e.g. Michael, cannot stop Satan from doing iniquity, but invokes name of God to stop him (Jude 1:9), because, unlike Jesus, Michael is not God, but just a servant. But Jesus heals, and expels demons, by His self-sovereign will and initiative, without praying to any principle above Him, for He, alongside with the Father, is the highest Principle, for He and Father are one (John 10:30). Thus, this word of Jesus, so far as it possesses divine self-sovereign authority, is eternal.