"bạn" is for whoever you consider friend and/or you're on the same social level. "em" on the other hand indicates someone who is younger than you (either male or female) or with "lower" social status.
In a relationship (marriage), the male partner is automatically called "anh" and the female partner is automatically called "em", regardless of age. As in this sentence, it indicates that this is a male partner saying to his girlfriend/wife.
I understand kinship terms, i hate how duolingo is lacking them, apart from this.
I get this is a popular song, but afaik you don't mix up anh-em and tôi-bận, unless you want to be poetic (or rude?).
I see mixing on those terms happens only in songs, but i haven't really mastered what kind of nuance it is conveying.
So, does it serve other purpose than just being poetic (use tôi with em)?