The way I heard that term first time, long, long time ago, it was player versus player and player versus environment. But the context was multiplayer, massive multiplayer online role play game, to be precise.
mmorpg servers could be split into pvp and pve, where you can attack other players without their consent on pvp, and only with consent on pve servers.
The way I perceive the terms nowadays, pvp is used to indicate competitive multiplayer. For "pve", the more popular term used is coop/co-op.
The term(s) probably evolved. Maybe not as bad as rogue-like. But I never heard pve used as a synonym for single player.