So it depends
From LongMan dictionary:
A teacher is someone whose job is to
teach, especially in a school.
A professor is a teacher of the highest
rank in a British university, and is a general term for a teacher in an
Someone who teaches in a British university and
who is not a professor is called a lecturer.
A tutor gives
lessons to just one student or a small group of students, especially privately
in their home or a student"s home.
An instructor is someone who helps
people learn a sport or practical skill, such as driving, skiing, or swimming.
A coach is someone who helps a person or
a team to improve in a sport
A trainer is someone who teaches people
the skills they need for a job. It is also someone who teaches skills to
From the US Bureau of Labour Statistics:
The ranks are instructor, assistant professor,
associate professor, and professor. Colleges and universities usually hire new
tenure-track faculty as instructors or assistant professors under term