Technically, yes, although I think it depends which “version” of English you speak. Certainly not “tooth grease”, however.
Here in Canada, we don’t typically use the word “paste” to refer to adhesives (“glue” is much more common), but I know our U.K. friends do say “paste” when talking about glue - so it’s all a bit… uncertain. It makes me wonder if it seems weird to people of the U.K. to hear or say “tooth paste” - which to you folks must literally mean “tooth glue”.
I think this is the crux of the “thermal paste” conundrum. When I read this combination of words, I force myself to assume they do not mean “thermal adhesive”, but rather they are simply incorrectly referring to thermal grease/compound as “thermal paste”. However, sometimes people really do mean “thermal adhesive” when they say “thermal paste” so I am probably fucked one way or they other.
Which is why I love the terms “thermal compound” and “thermal adhesive”. There’s just no doubt what they mean, regardless of what version of English one speaks.
(There’s a joke about Brits’ teeth in there somewhere, but I held back the effort to find it.)