brandmark vs trademark

brandmark is not a noun while trademark is a noun.

Word	Noun	Adjective	Verb	Adverb
brandmark	No	No	Yes	No
trademark	Yes	No	Yes	No

As verbs, brandmark and trademark are synonyms defined as:

Other synonyms of brandmark include brand.

brandmark (noun)	trademark (noun)
	a distinctive characteristic or attribute of someone or something
	a formally registered symbol identifying the manufacturer or distributor of a product

brandmark (verb)	trademark (verb)
mark with a brand or trademark	register the trademark of
	mark with a brand or trademark