company union vs brotherhood

company union and brotherhood both are nouns.

Word	Noun	Adjective	Verb	Adverb
company union	Yes	No	No	No
brotherhood	Yes	No	No	No

As nouns, brotherhood is a hypernym of company union; that is, brotherhood is a word with a broader meaning than company union:

company union: a union of workers for a single company; a union not affiliated with a larger union
brotherhood: an organization of employees formed to bargain with the employer

Other hypernyms of company union include labor union, trade union, trades union, union.

company union (noun)	brotherhood (noun)
a union of workers for a single company; a union not affiliated with a larger union	the feeling that men should treat one another like brothers
	people engaged in a particular occupation
	an organization of employees formed to bargain with the employer
	the kinship relation between a male offspring and the siblings