They are very similar, but there are a few differences.
If you educate someone, you need to educate them ABOUT a particular topic.
- "I will educate you about the dangers of smoking"
If you teach them, you can use the same kind of sentence:
- "I will teach you about the dangers of smoking"
but you can also teach someone HOW to do something:
- "I will teach you how to swim" or "I will teach you to swim
but this is wrong:
- "I will educate you how to swim" or "I will educate you to swim"
"Educate" usually implies something more formal, like a school, while "teach" can be formal or informal.