I've seen both of them used as "to explain" or "to interpret", but I am not sure if there are differences in connotation or anything else?
Both can function as noun or verb. The basic difference is that 讲解 is "oral explanation", or "to explain orally", whereas 解释 simply means "explanation" or "to explain", and can be oral or written.
老師在課堂上講解得很清楚。 “The teacher explained (it) very clearly in class." (orally)
老師在課堂上解釋得很清楚。 “The teacher explained (it) very clearly in class." (presumably orally, but not spelt out)
課本第十頁解釋得很清楚。 ”Page 10 in the text book explains (it) very clearly."
讲解 = 讲 + 解.
Literally, 讲 means to talk, speak, and say, etc, and 解 means to solve, understand.
解释 = 解 + 释.
释, as far as I know, its' more like a Buddhism word which means to explain some profound idea and guide you to understand it.
Basically, when you mean someone tell you something orally, you may use the former one if you are saying "Somebody explained something to me orally".
The later one can be used in a wider range of situations since it does not limit the way you've been explained.