roshanarose....In my experience, "full professor" is a rank given by a university or college and includes tenure, etc. It is up the academic ladder, but below, say, a Dean. There are entry and other positions below that, and my guess is that the lowest would require a masters' degree as a minimum. So, the various levels of academic rank would require a masters degree, but lots of people have masters degrees who are not professors or assistant/associate/adjunct professors.
More information here. http://en.wikipedia.org/wiki/Professor#Canada_and_the_United_States
[When I was a staff reference librarian at the Univ. of Iowa, much laughing/ rolling of eyes was done by senior faculty when a new faculty member, who'd just gotten his Ph.D joined the staff...and was listed in the city phone book as Dr. First Name, Last name. People were laughing at him right and left since the President of the University, with many distinguished degrees to his name, was listed in the same phone book as Willard Boyd. Another one, with the ink still wet on his Ph.D. always signed his name with a flourish...Dr. James J. [Last name], Ph.D. We'd almost laugh in his face when he handed us his card. PLEASE!! We had incredible faculty members known for their fantastic research, and this "young pup" thought he was so high and mighty. The higher up the academic ladder and better known in their field the faculty were were, the more humble they were, it seemed.]
jane