trademark vs brandmark

trademark is a noun but brandmark is not a noun.

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

As verbs, trademark and brandmark are synonyms defined as:

Other synonyms of trademark include brand.

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

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