like hell vs like mad

like hell and like mad both are adverbs.

Word	Noun	Adjective	Verb	Adverb
like hell	No	No	No	Yes
like mad	No	No	No	Yes

As adverbs, like hell and like mad are synonyms defined as:

like hell and like mad: (informal) with great speed or effort or intensity; used for emphasis

Other synonyms of like hell include like crazy, like sin, like the devil, like thunder.

like hell (adverb)	like mad (adverb)
(informal) with great speed or effort or intensity; used for emphasis	(informal) with great speed or effort or intensity; used for emphasis
used ironically to indicate the opposite of what is stated