What are the neurological differences between varying types of love?
It is very difficult to offer a response in the sense proposed, different researchers may have very different views. One of the keys in these research is to have clear differences between: attachment, attraction, sexual behavior, esthetics (philosophical theme), likes, interests, and very huge etc.

One can begin by reading Neil R. Carlson's chapter about reproductive behavior (Carlson, pp. 319-366) which addresses both hormonal and neural control of sexual behavior as well as maternal behavior from basic and general psychophysiological approaches.