教授: The act of teaching and the professor consulted
Compare 言語学を教授している with 研究室の教授に to distinguish ongoing teaching from the professor consulted about a thesis.
The act of teaching linguistics
教授 can refer to teaching or a professor. 「彼は大学で長年、言語学を教授している。」 describes teaching linguistics at a university over many years.
言語学を identifies what is taught, and 教授している describes the continuing teaching. Preserve the location and period in 大学で長年 without adding a particular rank or appointment procedure.
Consulting a professor as a person
「研究室の教授に卒業論文の相談をした。」 says the speaker consulted the professor in the research lab about a graduation thesis. Here 教授 identifies the person consulted.
The に in 教授に marks the person involved in the consultation. Consulting does not establish thesis approval or graduation, and this example is not a question about a form of direct address.
The noun and its verbal combination
The first sentence has 言語学を教授している as an act of teaching. The second has 教授に相談をした as consulting a person. Read the object and surrounding construction to identify each role.
The teaching use of 教授 should not automatically be treated as a particular university position. In these sentences, the relevant distinction is between the subject taught and the person consulted.
Do 教授 in 言語学を教授している and 教授 in 研究室の教授に refer respectively to an action and a person?
Show the answer and why
Yes. The first construction describes teaching linguistics. The second identifies the professor consulted about a graduation thesis. Distinguish the roles through the words and construction around the same term.