Problem is we don't have a lot of definitive information on the Celts, and Aine isn't even really a major player in Irish myth, so we have little to go on.
I've never seen her associated with the moon though, I think that may be a more modern interpretation. Best I can give you is that she started out as a goddess of love and fertility, and later on was thought to be the Queen of the fairies by the people of Limerick (yes, it's a real place

). No real reason why she can't be both, though, love and fertility are often fairy traits.