Primarily the latter: FUN FUN FUN. Any isk from PvP is an added bonus. The only exceptions to this might be organised, for-profit, hauler ganking and whaling or killing of extremely expensive PvE/mission running ships. But even with those activities most people who do them do them for fun and I feel confident in saying that the vast, vast majority of people are paying to PvP, not profiting from it.
Mercenary work used to be an exception too but that’s another playstyle that has massively declined (Noir are the only people I know that supposedly still do it full time) and, similarly to all other PvP, profit is not necessarily the primary goal. Winning, building/maintaining a reputation and getting content all probably come first.