I'd definitely lump them together, ignore any distinctions, and strongly recommend avoiding all of them.

I mostly do but I'll sometimes use olive oil for salad dressings or low temperature sauteing and coconut oil for higher temperature frying. I prefer butter or lard for low / high temperature frying respectively though.

Effects of unrefined sugar differ somewhat from effects of refined sugar too - still, the only sensible thing is to cut both.

Yeah, sugar's pretty bad in most of its forms. I don't worry too much about sugar intake in the form of raw fruits and berries (which I eat a lot of) though.