No, these words are not exactly the same. In some ways, an explanation can be someone else's interpretation of some information.
When someone interprets, he/she receives information and comes to his own conclusions about it.
When someone explains, he/she gives his conclusions to others, who interpret the explanation for themselves.
These are just the nouns of these two verbs that are very closely related. The tricky part is that you can also receive explanations, and also give interpretations, and I think that is what confused you.