professor vs academic

professor and academic both are nouns.

Word	Noun	Adjective	Verb	Adverb
professor	Yes	No	No	No
academic	Yes	Yes	No	No

As nouns, academic is a hypernym of professor; that is, academic is a word with a broader meaning than professor:

professor: someone who is a member of the faculty at a college or university
academic: an educator who works at a college or university

Other hypernyms of professor include academician, faculty member.

professor (noun)	academic (noun)
someone who is a member of the faculty at a college or university	an educator who works at a college or university

professor (adjective)	academic (adjective)
	associated with academia or an academy
	marked by a narrow focus on or display of learning especially its trivial aspects
	hypothetical or theoretical and not expected to produce an immediate or practical result