I think in this song the word darlin' simply means a person who is very dear to another. It doesn't necessarily have to be someone of the opposite ***, just someone who will stand by you and support you when difficult times come. I haven't seen the movie, so I can't comment on how the word is used there.
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Blue JayI have always simply assumed that the song was addressed to a woman.I agree. That is the assumption that almost everyone would make. It is highly unlikely that it means anything like "fellow".