I would say it becomes an abstraction when it needs parameters in addition to the nominal arguments. So in the case of "addThreeTimes(i)", sure, that's just abbreviation, but "addNtimes(i,N)" is a bona-fide abstraction.

Edit: Reminds me of the distinction between inheritance and subtyping: https://www.cs.utexas.edu/users/wcook/papers/InheritanceSubt...