—“One who professes, avows, or declares”
— “a faculty member of the highest academic rank at an institution of higher education”
definitions by Merriam-Webster
A PhD receives the title Doctor, specifically a Doctor of Philosophy.
Through the Middle Ages, professors began to study, teach, and debate on other subjects besides theology. As disciplines grew, so did universities.
Medical doctors earned the title Mr. until recently, because at first, they only received an undergraduate degree and then apprenticed. As they began to study the human body in more depth, their schooling eventually reached the same level as PhDs, thus earning the Dr title.
In the United States, high school teachers are licensed by the state to educate students in a specific subject or in a specific age range. They undergo training in their subject, childhood psychology, and pedagogy, the study of education. Teachers usually apprentice with a more senior teacher, before entering into their own classrooms.
Professors are academic scholars, who study a particular discipline. They engage in original research, which they write, present, and publish on this research. They are asked to teach undergraduates about their subject matter. They receive limited training on teaching and are not licensed to teach in the state.