Is one more formal then the other?
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Teach is including a more general concept.
According to Longman Dictionary of Contemporary English
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Also you may find it interesting to know:
Professor is more specific of teacher, as it is used when referring to a teacher of the highest rank in a college or university.
Informally, professor is used to refer to any instructor, especially the specialized ones.
[Reference: the New Oxford American Dictionary.]
Professor is also a rank, and a title, in the American university system and as such, confers status on its recipients. There are lots of "instructors" and "lecturers" and "graduate assistants" who teach and publish original research who would love to be called "professor." So yes, "professor" is more formal than "teacher." In any sort of professional setting, for example in asking for the referral of an article or seeking university employment, I would be very careful to refer to the professor I'm mailing as "Professor" and not "teacher", so as not to seem overly familiar.
I believe a 'teacher' is someone who teaches you anything. 'Professor' is a specialist in a field of study and teaches by profession.
A mother can be a teacher but not a professor (unless she is falls into the category mentioned above).
A professor is one who teaches in a university or college whereas a teacher is the one who teaches in high schools and comprehensive schools.
protected by tchrist Feb 21 '15 at 23:56
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