Traditions around academic titles, and the like, differ greatly from country to country and are heavily bound and conditioned by culture, history, language, etc. For U.S. usage and practices around these concepts, I can give you the following guidelines:
1. Ph.D. is an academic degree, whereas Professor is a title and in fact technically a specific rank. Typically full-time, tenure track, academic faculty members begin as Assistant Professors, get tenure and are promoted to Associate Professor, then achieve the rank of (Full) Professor when they've attained a very high status at their universities and in their fields.
2. In a university setting, you can be (and are) called "Professor" without having a Ph.D., as the two things (degree vs. title or rank) are only loosely related.
3. Most students at U.S. universities will refer to a given teacher as "Professor ____" regardless of the person's precise degree or rank.
4. You wouldn't normally refer to someone with a Ph.D. as "Professor ___" outside of an academic context. You might hear "Dr. ____" in a corporate setting, for example, but even that's a bit unusual.
There's much more to this, but hope this helps.
PS: I have a Ph.D. (in International Political Economy from the University of Southern California and at one time was a full-time faculty member at the University of Florida).