PhD usually makes one a professor.
Tenure is granted based upon time at a particular university and performance. Some universities also require professors to be "published"....books, studies, etc....before granting tenure.
Not necessarily true......a "professorship" is granted by the Department Chair of an institution based on criteria that is unique to each institution/department. There are a number of types of professorships, and although a PhD, MD, or JD are generally required, there are many granted the title that have none of the mentioned degrees, and I know of several that have no degree at all. Unlike the public school system, there are (generally) no statutory academic requirements for instructors at institutions of "higher learning", unless the requirements are established by the institution itself.
A "professorship" further does not always mean that the individual is a full-time employee of the institution.......my daughter-in-law has just been named "Professor" at Cornell University Law School, and although she does teach courses there, she is a full time employee of a law firm several hundred miles away.
Your analysis of tenure is generally correct, depending on discipline........however, tenure can be granted without any of your stated criteria, if the individual has accomplished outstanding performance in areas outside of academia, and hired on that basis.
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