Hope, as it is used in Greek is really more of an expectation or anticipation of a sure thing. In English, a hope may or may not happen. So I prefer to substitute “expectation” in almost every case.
The short answer is “Christ in you folks is the expectation of glory,”
as in the glory cloud filling God’s habitation.
Right at the beginning of Hebrews, we learn the reality is “in Son” (Heb 1:2 when the extra-added words are removed). Then Heb 1:3 explains the Image of the Son.
By the time we get to Heb 10, the beginning of the chapter talks about “a body you have prepared for Me” (Heb 10:5). This is about the “True Temple” that we are all being built into as spiritual stones. Again, the expectation is Christ within you people, the expectation of His glory filling His temple / body that we are.
Then in Heb 10:20 we learn of this way Jesus initiated in us, for us, with us … all those implied dative prepositions. Sadly, the typical translation calls it a “new way”. The kind of “new” is that characteristic of a freshly slain body…like a little lamb. Think of Rev. 5:6, “I saw a little lamb as slain, but standing.” There is a governing nature of Jesus that penetrates the veil, taking us with Him like the High Priest wore the ephod on the breast.
And that is the kind of priest we have over God’s household / temple / house that He fills (Heb 10:21).
Thus, since He went in and penetrated the veil by His own fresh blood with us borne on His breast, we can come to interface with Him in the Holy of Holies (Heb 10:22). Heb 10:22 is sort of a restatement of Col 3:1-4 and Eph 2:6. The corporate risen body’s head is in heaven governing from the Right Hand and we are on earth connected by this “way”, this “slain Lamb,” “Christ-crucified” nature. It is this “weakness of God” that overcomes the “strength of men” (1Co 1-2). Thus, we are sprinkled clean by Who He is, not what we do.
Thus, in Heb 10:23 we are continually saying the same thing in the same place (confessing), retaining the same “Logos” = the same underlying matrix that reckons how things are, which can be a communication or The Communication as we see in Heb 1:3. If we maintain, the “in Son” thesis of Heb. 1:2 all the way through the book, then the Expectation is Christ in us! He is faithful!
Is this the same Expectation as in Heb 6:19? Yes, the “in Son” theme fits each and every aspect of Hebrews. He is our Expectation as the head we are to tightly lay hold of as the body (Col 2:19). Or as Heb 6:19 says it, the anchor of our soul life is Christ crucified, the slain little Lamb standing, Who went behind the curtain into the Holy of Holies.
Thus, the anchor of our soul is not that I have a “J-train ticket” when I die, but that my soul has union right now with Jesus as Head of a body-temple that we are spiritually being built into.
So is John sating the same thing in 1Jo 3:1-3? Yes. We are called “children of God” in1Jo 3:1, or as Hebrews 2:13 says it, “the children and I”, which refers to Heb 2:10’s, “many sons into glory”. The world system does not know us in this way because it does not know Jesus in this way.
Then in 1Jo 3:2, John declares we are the sons of God even though we look like other people to outsiders who see other people only by their senses. This is like what Paul said in 2Co 5:16, but in sort of an inverse way. Paul said we do not know each other according to the flesh, nor do we know Jesus that way anymore. Rather, because we are “in Christ”, a corporate risen body, it is a new creature-creation (2Co 5:17). A new creature as a new head – back to the point Paul made in Col 2:19.
Then John continues in 1Jo 3:2, when Jesus appears – not known in the flesh – but in this different way of the spirit, the we shall be like Him due to the fact that we perceive Him “down exactly how” He is. This again is like what Paul said in 2Co 3:18 about beholding as in a mirror and being transformed into the same Image. I think this is also the meaning of Heb 2:9, which I have already noted has alignment with 1Jo 3:1-3 above. You see, in the first part of Hebrews, the author(s) compare Jesus “as He is” with a bunch of Bible characters that a Jew would be tempted to hold in higher esteem, which includes angels. “But we see Jesus…” (Heb 2:9 KJV).
Thus, in 1Jo 3:3, everyone having this expectation = Christ in you people being the expected glory cloud in His own temple (Col 1:27) and Christ our life appearing (Col 3:4), then we should let die those parts of this risen body that are earth bound (Col 3:5). Again this is exactly what John is saying, but in sort of a reverse way, “set yourself apart “down exactly how” He is set apart or as KJV says it “purifieth himself, even as he is pure.”
The expectation of Jesus being the life of His body naturally excludes my soul life expressions on earth. In fact, Jesus always said this. No person can even be a disciple – cannot even follow – unless they ruin and destroy way, completely off, the soul-life. (Luke 9:23-26, Mat 10:37-39, etc.)
Why such harsh reality?
Because Jesus designed-created our souls for His life-Image-Likeness. As Gen 1:26 has always said, people are designed to bear God’s Image, which we would have zero clue about, had it not been for Jesus coming to earth, going into kenosis (self-emptying), being that little lamb going to slaughter – that one Lamb that did when to the altar in Isa 53 while we all as sheep went astray. Jesus was obedient unto death on a cross. That is the kind of “new way” is the very kind that pierced the veil of flesh. It is how we know Him and how He is the anchor in any circumstance or situation on earth.
So yes, all three Expectations – Hopes are all about Jesus simply
being the life in His risen, united body, the church.