While I think that teaching has a clear meaning, education could refer to teaching (doing the educating) or being/getting educated. I'd suggest that the tag teaching be renamed education-teaching and that the questions tagged as education should be retagged as education-teaching or education-learning as appropriate. What do you think?
Four years later, this still isn't resolved: we have separate tags education (928 questions) and teaching (392 questions). At first glance, they look different because education would include learning as well as teaching. However, both tag wikis explicitly include teaching and learning:
Mathematics education consists in the practice of teaching and learning mathematics, along with the associated research. Research in mathematics education concerns the tools, methods and approaches that facilitate the practice of mathematics or the study of this practice.
Questions related to the teaching and learning of mathematics.
I see that the first also includes research in Mathematics Education; but such questions are actually rare on the site. They would be better asked at Mathematics Educators anyway.
I propose to
Note that being a tag synonym is not the same as "synonymous" in ordinary language. Tag synonyms are not symmetric: rather, they mean that when a user tries to add tag A, tag B is added instead.
Include a mention of Mathematics Educators in the tag wiki
For example: "Some such questions may get a better answer at Mathematics Educators".