Are '고맙습니다' or '감사합니다' interchangeable, or is there a difference in meaning or politeness?
감사합니다 is slightly more polite/respectful than 고맙습니다. As far as I understand, this is mostly just because "that's how it is" and not the direct consequence of the literal meanings.
That said, there are differences in the actual meaning of the words.
감사하다 is an action verb (동사), which literally implies the speaker doing the action of thanking.
고맙다 is an adjective (형용사), which describes the state of being thankful/grateful.
- 고마워하다 is the action verb (동사) version of 고맙다.