Getting back to jeanne's original question, I think there is a fourth (third? lol) "type". I love, because I love.
I was just thinking about Master and trying to fit him into one of the catergories, but I can't. I love him because I love him. The end.
I could give you a list of things that I love about him, but that wouldn't explain WHY I love him. (I could also give you a list of things that drive me nuts, but that is neither here nor there....) I love him just because I do.
If you expand your definition of love beyond the romanitic type (and assuming that you do in fact believe in love) and ask yourself why you love your parents? Your siblings? You children? It is probably not something you can explain. You just love them.
I love Master.
I love my family.
I love my friends.
I love my child more than life itself.
I love Candy Cane Chocolate Fudge Crackle ice cream.
Why does it have to be any more complicated than that?
[I have had a couple of glasses of wine this evening.... apologies if this post makes no sense at all.]