Is there a consistent way to identify that a girl is a girlfriend? Would it be the presence of "a chailín," "his girl" that points to it?
"girlfriend" is a relatively new invention in English, and Irish hasn't had any need to develop an equivalent. cailín means "girl", and whether you prefer to say "his girl" or "his girlfriend" when referring to what the NEID calls a "romantic companion", is up to you.
The a in a chailín just means "his".