you would grease the pan with butter or lard before cooking
Likewise, Helen, but that's a verb.

Vegetable oils advertize that food cooked in their oil doesn't taste greasy.
Likewise, but that's an adjective.

i have used "crisco" a brand of solid vegetable shortening (solid oil!)
Yes, we have solidified oils, but we would probably call them "lard" (or just "fat").

I suppose we fail to distinguish between oils that can solidify ("grease" to you) and oils that don't (and therefore remain "oil" to you).

Weird, isn't it? All these things we take for granted, and that are just so everyday we can't imagine any different kind of perception/language.

P.S. We'd talk about draining of all the fat or oil except x spoonfuls, though we do talk about "dripping". You used to be able to buy beef dripping, in fact, and it served as a quick snack spread on a slice of bread.