The terms bemerklich and bemerkbar are certainly very close in meaning. I could not think of a situation where only one of them, but not the other, would be applicable. Are there any?
It also seems this is a particularity of these two words and does not generalize to many other x-lich / x-bar pairs, or does it?
Edit: Several commenters pointed out that the term bemerklich is unusual. Google finds 260k hits for the term, and ngram shows it as similarly common as bemerkbar until around 1870, then declining. dict.cc also demarks it as veraltet. It seems the term is not in common use anymore; I probably picked it up from old literature and according set expressions. (Ich bin Muttersprachler.)