Hello Again Old Friend
I often feel that I've changed so much over the years that I'm not really "the same person" in a meaningful sense as I was even two years ago, let alone ten or more.
However, something really lovely that's happened to me multiple times over the years is reconnecting with very old friends who I'd completely lost touch with, and finding that we get along really well (again).
Since some of those friends also say they feel like "a different person" from who they were when we met, there's actually something weird about this.
There's a couple of "easy" explanations:
1) We haven't changed nearly as much as we think we have, so basically it's the same two people being friends again and there's no big mystery;
2) We've changed a lot but there's some unshakeable "core" to each of us that made us friends then, and makes us friends now.
3) Actually it's selection bias – while I haven't seen these old friends in X years, I only end up re-meeting with a non-representative subset who are unusually likely to be the sort of people I like spending time with now. (And if I re-meet someone and we no longer get along, they drop back out of my life and don't seem as salient).
All of these might be part of the truth, but I have a fourth explanation that I find much more interesting:
4) a large part of friendship is "expectation of friendship" – if you're confident someone likes you, and is going to act friend-ly towards yo, then you'll be more open and vulnerable and supportive with them... which will make them more likely to like you, and more likely to be your friend. Meeting up with a very old friend gets you both started at a really positive equilibrium and your new friendship becomes a self-fulfilling prophecy, even if you've both changed so much that it's like two new people having a whole new relationship.
[editorial note: this post is self-plagiarized from something I wrote ten years ago, as a few of my posts here are – in this case it seems relevant that I still identify with it!]