"Differential diagnostics"

Sometimes the use of the adjective (or flat adverb) instead of the regular adverb is possible, but significantly changes the meaning of the sentence.

Act shy vs. act shyly:
"if someone is acting shy they're acting as if they were shy, and if someone is acting shyly they're acting in a shy manner"
from the LEO forum, quoting a British native speaker, comments 14-21

Act weird vs. act weirdly:
"If somebody is acting weird, than this person behaves in a weird way, or acting as if they were weird. If they are acting weirdly, then they are either behaving in a weird way as well or they are an actor performing in an unusual way."

Go crazy vs. go crazily":
"If somebody is going crazy they are becoming crazy. If they are going crazily they are moving forward in a weird/crazy manner."

Act different vs. act differently:
American native speaker 1 (LEO forum):
In my day-to-day (informal) communications, I'd usually say "He acts different than me"-- if I mean that his behavior is different from mine. Of course, I'd say "He acts differently than I do"-- if I mean that we are both actors and we have different acting methods or styles.

Think different vs. think differently:

American native speaker 1 (LEO forum):
"He thinks different than I do (on that issue.)" (We disagree on that issue.) In contrast, "He thinks differently than I do" might mean, for example, that he reads everything he can about the subject and then prays about it, etc., before making a decision -- whereas I simply ask the neighbor boys what they know about the subject and then do whatever they recommend.

American native speaker 2 (LEO forum):
"Think different in the sense of "think something different" (and not what everyone else thinks). Think differently would mean "think in a different way," i.e., how you think, not what you think. But there is considerable overlap, IMO."