It's the same person. It's always very much the same person. Yet, there is something stilted about how they write... you can tell they're being a little more prim and proper, holding back a little, measuring their sentences. Then, gradually, you both begin to loosen up a little. You look at the communication and see that you're starting to pick up some of each other's vernacular-- favorite words and expressions. (At least, this happens with my friendships, because I tend to use made-up words and the people I gravitate towards also are creative in this way. ;)) Even things like punctuation might change a little, because one or the other of you decides you like the way the other person does a thing better, and you start doing it yourself. (Example: before knowing Amy, I always did...this, instead of doing... this. The space, you see, after the "dot dot dot.")
It just puts a smile on my face, to look back. To see where we started, what we talked about, what mattered then. To wonder where we'll go, what we'll talk about, and what else will matter. To wonder what will change, and what will stay the same. To realize that you and the other person have created something together that never existed before, as happens with all close human relationships. That's what makes them exciting. Each time you discover a dear friend, you discover parts of yourself that you never knew existed.