It's difficult to give a simple answer to that because they have so many uses. However, I would say that 'as' is close to the verb 'to be' and 'like' means 'similar':
She gave her opinion as a doctor.
he gave his opinion like a doctor.
In the first, the woman is a doctor, but in the second, the man only spoke in a way simialr to a doctor, but isn't actually one.
- For Teachers