What are the different types of tropism

Well,

One could add many different prefixes to tropism to get various results.

Photos + tropos = Phototropism = Turning toward the light.

Gravi + tropos = Gravitropism = Turning toward gravity, a.k.a. turning downwards.  Plant stems exhibit negative gravitropism, as they grow upwards, against gravity.  I would call it "graviphobia."

Hydro + tropos = Hydrotropism = Turning toward water.  This is exhibited by plants' roots growing toward water.

Those are the ones that you can look up in a dictionary and find as legit words.  These are ones I have just made up, but still make sense (to some degree).

Helio + tropos = Heliotropism = Turning toward the sun.  Synonymous with phototropism.

Claudo + tropos = Claustropism = Turning toward enclosed spaces.  Sounds silly, but that's what you do to go into an elevator.  Synonymous with claustrophilia.

Caput + tropos = Caputropism = Turning toward the head.  That's what everyone does when they face the leader of their group.

Astra/stella + tropos = Astrotropism/Stellatropism = Turning toward the star.  Basically stargazing.