vertical union vs brotherhood

vertical union and brotherhood both are nouns.

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

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

vertical union: a labor union that admits all workers in a given industry irrespective of their craft
brotherhood: an organization of employees formed to bargain with the employer

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

vertical union (noun)	brotherhood (noun)
a labor union that admits all workers in a given industry irrespective of their craft	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