Okay, today in Gelfin's Word Nerd Corner, we'll once and for all dissect "Think Different." Everyone seems to think that Apple's venerable slogan is grammatically flawed. "You mean 'think differently,'" one is tempted to say.
But that's just wrong. "Think differently" does not express the idea they want to convey. They're not suggesting that your thinking should be different. What they're saying is, "given the many qualities you might consider when evaluating computers, we suggest you consider ours because they are different."
It might make more grammatical sense to you if it were written
Think "Different"
...but that doesn't really exactly work either, because they don't want you to think about the word different. They want you to keep the concept of "different" in mind when shopping for a computer.
The slogan might make more sense to some people if it were extended like this: "Think Different. Think Apple." The parallelism here makes the implication more clear: "Apple is Different."
To summarize, "Different" is not an adverb in this case. It's a noun direct object of "Think." This is a somewhat idiosyncratic usage in English, where "Different" is a shorthand for "the idea of Difference," but it's perfectly valid.