Pretty self-explanatory.
Kill quests are obvious enough.
Collection of items – removed after completion or just gaining that amount.
Skill quests – attaining a level or achieving a set amount of experience gains (perhaps of a minimum amount).
Exploration quests – visit / walk a set amount of steps in a named area. Go to a specific co-ord point. Find the fishing spot.
I’ll rattle off more later but just throwing this out to evoke some discussion and input.