In my opinion tutor " means "

Private teacher who teach their students in their home or instead of students house . Sometimes tutor have their own coaching centre for teaching their students.

But we use both teams as a teacher .

But teacher ""

Means another way you can say

Those who are teaching in school . like some institute .

Teacher is a bit more formal than a tutor.

In the context of high school or college, a teacher is the one who is actually teaching you the class. In high school, you call teachers "Mr. [Last Name]" or "Ms. [Last Name]" and in college, you call teachers "Professor [Last Name]."

A tutor can be someone informal who helps outside of normal class time. Maybe you take supplemental classes with a tutor at night, for example. Or a tutor can even be your classmate, taking the same class as you, who really understands the material well. In any case, usually, teachers have a higher educational level than tutors.

On this site?

Teachers have certificates and such to prove mastery of languages and how to teach them.

Tutors know the language, but do not have necessary paperwork to show the mastery of the language.

That is not to say teachers are smarter than tutors.

Some teachers are also tutors in other languages.

Tutor is usually a private teacher who teaches small groups or individuals. So in an elementary school, you have teachers because they are not hired by students’ parents and they teach large groups of people.

plus, you can use tutor as a verb!

'Tutor' is one of these designations which can have many roles. A tutor may give additional out-of-school instruction to a student, in which case (s)he is probably a very well-qualified teacher. At some universities in England you may be assigned a tutor who will oversee your general academic progress ; again, such a tutor will be a highly-qualified teacher of the university.

Many professional teachers on Italki are well-qualified teachers of English as a second language, and this type of teaching is their main occupation. On Italki 'community tutors' are usually enthusiastic well-qualified native speakers of their language. They may not be qualified second language teachers, but they can help you with your learning. They are also often cheaper than 'professional teachers' on Italki.