The way I remember it is that all three names are based on the image and codomain since the arguments/domain are total.

Sur- means 'upon' (sorta) as in sur-la-table, so we know the surjective is upon the entire codomain, hence surjective is the 'at least once' class, leaving injective as the 'at most once' class.

Bijective is the invertible one but I've never had problems remembering that and I note that you don't mention it either.