What's the difference between English teacher and English tutor?

It’s a different job. Teacher means you teach in school with a larger class, tutor usually means one or a few students, or a smaller class that’s in addition to the usual class. 

A teacher teaches. That is, lesson plans, structured curriculum, classroom, extensive amount of time, original material. Qualifications to teach according to local standards of certification. It varies by location. A teacher can have other tasks of attendance and grading. A tutor helps to improve performance. A tutor is generally private and not certified. A tutor is only concerned with subject matter.

An English teacher teaches the english language.
 A Tudor is a member of an English royal dynasty of Welsh origin which ruled England from 1485 to 1603.