***Neither a teacher nor a native speaker.***
Hello my dear,
I believe I can understand the sense.
You don't focus on the word think here.
Let's say someone has a stupid way of thinking.
In this case I would say, "He thinks stupidly."
But let's say that someone thinks about something modern.
So all their thoughts focus on something that is modern.
"He wants to invite some new product, so he thinks modern."
I guess it's the same for "Think different."
In Germany we have some video spots that are about cars and their efficiency.
They do not have such a high emission, which is good for the nature.
It's called "blue efficiency".
In the video spot they say, "Think blue."
Sorry that I could not give you a real answer, though.