A Hebrew teacher may be one of the 2 categories:
Teacher of Hebrew
The technical differences are extremely small and yet valuable when making your decision. Hebrew teacher teaches Hebrew to Hebrew speakers, when a teacher of Hebrew teaches Hebrew as a second or a foreign language.
Unlike a Hebrew teacher (or a teacher of German) a tutor usually doesn't have a college or university degree in teaching, education or linguistics.
Tutors often use unconventional and more cultural methods of teaching. tutors tend to focus on student's experience and language natural development rather than typical books.
A teacher can teach you grammar, structures, time tenses and a tutor can help you expand your vocabulary and dip your toes into culture, however...
Practicing with Hebrew Native Speakers helps you improve on pronunciation and understanding of a fast, real, dialectic speech, especially giving that Israelis just love to speak so fast.