The terms aff. & cf. can be used by anybody although they are mostly used by taxonomists.
aff. ie affinis or affinity means closely related to.
eg. If you put a aff. x. IT means it is similar to ax, likely belongs to the same species group , but it is not sp x as far as you know.
cf. ie conferre or confer means to compare.
If you put a cf. x, it means it is very similar to ax with some minor differences & could be the same species, x.