half-breed vs half-bred

half-breed is a noun but half-bred is not a noun.

Word	Noun	Adjective	Verb	Adverb
half-breed	Yes	Yes	No	No
half-bred	No	Yes	No	No

As adjectives, half-breed and half-bred are synonyms defined as:

Other synonyms of half-breed include half-blooded.

half-breed (noun)	half-bred (noun)
an offensive term for an offspring of parents of different racial group (especially of Caucasian and American Indian ancestry)

half-breed (adjective)	half-bred (adjective)
(of animals) having only one purebred parent	(of animals) having only one purebred parent