I'm not an expert but I believe he was a spirit for awhile and inhabited other bodies, so he's not a zombie, but actually a spirit that just inhabits his original body (and can heal it etc), but can also possess/take over other bodies as well.
Also shooting him/hitting him in the head doesn't take him out/down like a zombie. Burning him doesn't destroy him like a zombie etc. His only real weakness is putting him to "sleep" under his lake, which doesn't kill him, but just stops him (I guess till they make another movie hehe).
Also, he doesn't kill indiscriminately, he won't kill kids, and even let some adults live once or twice. He goes on killing sprees and generally seems to hate horny teens (lol), often killing them in extremely painful ways for the fun of it (or audience appeal I guess), but he doesn't kill every living thing he comes across. A zombie is ravenous and does not choose it's victims. Jason also is smart and can think, plan, set traps, climb stairs, open doors and zombies are pretty much brainless (which makes their weakness kinda funny hehe).
So no, Jason is not a zombie.
He is a Chaotic Neutral spirit of Vengeance, with an aversion to sex.
Proud member of the Arv The Great is great fan club!!! Join today by putting it in your sig.