Don't think you can just become a Kohen out of the blue...so yeh...most likely all cohen's today are decendents of Aaron...
Most are, but it could be that some aren't (expecially in the Bukharian/Persian communities) In the Bukharian community maybe 30% say they are Kohanim, which is hard to believe, so either 1 of 2 things happened, either the population that was taken there was from places that are heavily populated by Kohanim (Jerusalem or Hevron) or that many made it up or believe themselves to be when they are not.
I myself was not told by my father (or uncles) that we are Kohanim, but I know someone (from my high school) who has the same last name to myself, said the same (blurry though) history of Great Grandfather and family (how they hid and ran away from the communist gov. and went to different cities, and how last name got changed) now that I know more like that my forefather was a great Rabbi, if I see him again I will ask him if we are the same family or not). The point- he says that he is a Kohen while I dont, so either we both are Kohanim and I dont know it, or we are Yisrael and he doesn't know it, or we are different family.
Or you could have had similar situations and his great grandfather was a kohen, while yours wasn't (ie different families).
Obviously if Tzvi and this guy just happen to share a name, i.e. not a father's line great grandfather, then one cannot draw conclusions from the other as to whether they are kohanim. And if one has no tradition of being a kohen, and the other has a tradition that hte is, it's likely that both are correct.
These expressions people have used, "Different family" and great grandfather, are a bit ambiguous. For example, one has 4 great grandfathers.
i'm not big on family trees.. so my reasoning may be at fault here, but I think it's fine.
The only father line that affects whether you are a kohen or not is one line. father, his father, his father e.t.c.
which is the same line that affects your tribe.
You are talking about a particular father line great grandather. Any other great grandfather is irrelevant to tribe and surname
So just sharing the same great grandfather is only relevant if that great grandfaher is father's line for both of you.
first cousins share a grandfather, (/parents are siblings)
but I only have the same tribe as the 1st cousins on my father's side.
second cousins share a great grandfather, (/the parents of second cousins are first cousins) but their tribe is determined by their father. Who is likely not even a relation of yours.