In High School only a bachelors degree and a teachers certification is required. If the high school teacher is teaching AP ( advanced placement) , DC ( dual credit) or IB (international bachelorite) they often have masters degree. To become a full time ,tenured professor at a major university you are required to have a Doctorate and often some type of research. Some community colleges and non-tenured professors can be professors with only a masters.
Now in High School teachers often see you very often and know you very well. They help you individually and understand your learning style. University professors often teach to large classes and only lecture. Ofcourse if you are struggling they can help you during their designated office hours.