bad-tempered vs ill-tempered

bad-tempered and ill-tempered both are adjectives.

Word	Noun	Adjective	Verb	Adverb
bad-tempered	No	Yes	No	No
ill-tempered	No	Yes	No	No

As adjectives, bad-tempered and ill-tempered are synonyms defined as:

Other synonyms of bad-tempered include crabbed, crabby, cross, fussy, grouchy, grumpy.

bad-tempered (adjective)	ill-tempered (adjective)
annoyed and irritable	annoyed and irritable