well-bred vs well-mannered

well-bred and well-mannered both are adjectives.

Word	Noun	Adjective	Verb	Adverb
well-bred	No	Yes	No	No
well-mannered	No	Yes	No	No

As adjectives, well-bred and well-mannered are synonyms defined as:

well-bred (adjective)	well-mannered (adjective)
of good upbringing	socially correct in behavior
	of good upbringing