bad-mannered vs unmannered

bad-mannered and unmannered both are adjectives.

Word	Noun	Adjective	Verb	Adverb
bad-mannered	No	Yes	No	No
unmannered	No	Yes	No	No

As adjectives, bad-mannered and unmannered are synonyms defined as:

Other synonyms of bad-mannered include ill-mannered, rude, unmannerly.

bad-mannered (adjective)	unmannered (adjective)
socially incorrect in behavior	socially incorrect in behavior
	without artificiality; natural