The word "mean" has so many meanings - as a verb meaning to intend, as a verb meaning to have a certain meaning, as an adjective meaning cruel, as an adjective meaning miserly, as a noun meaning average, and more - that it is absolutely impossible to answer such a general question without context. Both could be correct:
"That's mean" could be a sentence that uses any of its meanings as an adjective: "You kicked him. That's mean."
"That mean" could be a fragment that uses any of its meanings as a verb or an adjective: "What does that mean?" "Isn't that mean?"
You could also say "that's the mean," using any of its meanings as a noun: "That's the mean. This other point to its left is the median."
As you can see, a general answer to "what's the difference?" is impossible.