I remember the discussions that occurred that differentiated the term 'strong inference' from 'strong link'. The way it came across to me was that it was really a subtlety that made some sense in the context of some of the subjects that were being discussed at the time eg. Jeff described a strong link as having a strong inference and weak inference so presumably the idea was to have a term such as inference that distinguished between the potential strong/weak states of a parent strong link. Thus a pure 'weak link' is separated from the potential 'weak inference' of a strong link and so on.
Outside of that, I can't recall a situation in recent memory where the use of the terms 'strong link' or 'weak link' seemed to cause confusion. Unless there is some sort of confusion, using two different terms ie. 'link' vs. 'inference' doesn't seem all that necessary.