I was also taught (ala C.S. Lewis) that there were four kinds of love -
storge - affection, like for puppies and stranger's little kids or something
philia (friendship-love, based on mutual interests),
eros - y'know.
agape (Christian love, or charity [caritas], or goodwill, as in "goodwill towards men" from the carol).
less-basic synopsis here.
I always thought of what Ts and teachers and those sorts of folks feel for their clients/students, etc as somewhere between storge and goodwill, while what clients/students feel for them runs the whole gamut. But I also wonder if these kinds of distinctions are useful - I always feel like they leave something out.
....crazy?