So what's the different between "bad" and "badly"? I mean, when bad is use as an adverb.
They play badminton bad. (or badly?)
'bad' is an adjective, and 'badly' is an adverb. There are no exceptions.
"They play bad badminton" is correct usage because 'bad' is an adjective modifying the noun 'badminton'. "They play badminton badly" is correct usage because 'badly' is an adverb modifying the verb 'play'.
"They play badminton bad" is incorrect usage. However, it is often used lazily by native speakers who can't be bothered to say 'badly'.
Using 'bad' as an adverb is not incorrect, it is merely casual English. The forms found in casual English are NOT incorrect. Knowledgeable language sources realize this and make note of it.
You can feel free, Belly T, to use the adverb form of 'bad' in all casual language situations.
AHD: Bad is often used as an adverb in sentences such as The house was shaken up pretty bad or We need water bad. This usage is common in informal speech but is widely regarded as unacceptable in formal writing.
Usage note The adjective bad meaning “unpleasant, unattractive, unfavorable, spoiled, etc.,” is the usual form to follow such copulative verbs as sound, smell, look, and taste: After the rainstorm the water tasted bad. The coach says the locker room smells bad. After the copulative verb feel, the adjective badly in reference to physical or emotional states is also used and is standard, although bad is more common in formal writing: I feel bad from overeating. She felt badly about her friend's misfortune. When the adverbial use is required, badly is standard with all verbs: She reacted badly to the criticism. Bad as an adverb appears mainly in informal contexts: I didn't do too bad on the tests. He wants money so bad it hurts.
But what about the usage:
"They play badminton very bad"?
I've checked the dictionary, bad is also an adverb, too
The same rules apply to "good" when it is used as an adverb:
USAGE NOTEGood is properly used as an adjective with linking verbs such as be, seem, or appear:The future looks good. The soup tastes good. It should not be used as an adverb with other verbs: The car runs well (not good). Thus, The dress fits well and looks good. See Usage Notes at well2.
But, what's about :
We play badmintion very bad?
I see it regularly that formal English has this sentence
I never have. It is not formal English. Neither is it listed as acceptable usage in any dictionary I've ever seen. The Oxford English Dictionary does not even list an adverbial usage.
Using 'bad' as an adverb is simply incorrect. Just because it is used lazily in that way by some people does not make it correct - it sounds sloppy and uneducated. There is no good reason for doing so because there is a perfectly good adverb, and losing the distinction between 'bad' and 'badly' does nothing but make the language less precise. I think encouraging English learners to use sloppy vernacular does them a great disservice personally.