Yeah, from what I see, professors get their salary i.e. the money for living expenses from their teaching job. But most of the research money comes from grants. Those are usually earmarked so that they can only spend it for very specific purposes.

Edit: This is only true for people who need to run labs. For subjects like math or philosophy, professors depend less on grants since most of their work is done without significant expenses. But they still do need grants for travel and organizing conferences.