I think a master's of education and a master's of arts in education will be the same. Generally, there are two types of master's degrees: master's in arts and master's in science (there are other types of two-year degrees following a bachelors, but they're not really related to you question). A master's of arts (MA) is a master's degeree in a humanities field like history, art, or philosophy, while a master's of science (MS) is a master's degree in a scientific or technical field like biology, data analytics, or engineering. Some fields like psychology offer both MA and MS degrees. The difference is how much math and hard science you will learn. To know the difference between an MA in teaching and an MA in education, you should look at what courses they require. I assume the teaching degree will focus on lesson planning, curriculum design, pedogogical philosopies and things that are directly related to effective teaching and classroom managment (just my best guess). An MA in education might focus more on all the various aspects of an educational institution. Finding a specific program and looking at the courses they requrie will give you the best picture of the differences, if there are any.