As a primary school student I took woodworking classes and recall the teacher sharpening the gouges and chisels that we used on the lathe. I use the word sharpening but that is, perhaps an assumption. He ground and polished the cutting edges of the tools.
Years later in the workshop of a university department, I asked the instrument maker how sharp the cutting tools on the metal lathe needed to be. He said that he thought that hardness, not sharpness, was really the issue with metal lathe cutters, and then simply assumed that I fully understood what I'd been told.
And then yesterday, using a pair of old hair clippers, I caught myself wondering whether they needed sharpening, which reminded me once more of the sharp vs. hard distinction which I never did investigate. Does it make sense to talk about wood-lathe tools as being sharp as distinct from being hard, and vice versa for metal lathe tools? I can think of all sorts of ways in which wood is not like metal (!) but what are the differences that lead to qualitatively (as opposed to quantitatively) different characteristics of the cutting tools? ... and do hair-clippers get sharpened, or does the hardness of the steel versus the softness of hair solve all problems?