Japanese - English dictionaries translate both as "misunderstanding" or "wrong guess." Upon consulting dictionary.goo.ne.jp, I found:
誤解 - When the facts and the true intentions of a partner's words and deeds are shown to differ. Seems like when a fact was thought to do one thing and it does another.
勘違い - When the facts differ with one's understanding of the situation. Seems to be when you think something looks some way and in fact it is another.
Both seem to be pretty similar and probably are just versions of the same. On Weblio both seem to have similar meanings and example. Is there any particular nuance or are they both basically the same, like 誤る and 間違える?