This is not "no" meaning "not", this is another word: it means "not any".
Furthermore, this is a particular form of "any": it's an ADVERB, and it means: "even a small amount".
Since here we have "not any", it means: "NOT EVEN A SMALL AMOUNT DIFFERENT", or "IN NO WAY DIFFERENT".
As you know, adverbs "modify" the meaning of verbs, adjectives (like in this case with "different"), other adverbs and whole clauses.
However, keep in mind that the adverb "ANY" (or "NOT ANY" or "NO") is usually used with comparative adjectives (any faster, no better, etc). "Different" (not a comparative form) is an exception.