The only difference is the grammar. Varied is technically "past tense" (ie, "it has been varied"), while various is not specifically past or present or future, it's more generic. So, you can often swap these words without changing the meaning of the sentence. But sometimes it changes slightly. And sometimes one word just doesn't match the grammar of the sentence, so we need to use the other word. But aside from grammatical finesse, they have an identical meaning.