logo vs trademark

logo and trademark both are nouns.

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

As nouns, trademark is a hypernym of logo; that is, trademark is a word with a broader meaning than logo:

logo: a company emblem or device
trademark: a formally registered symbol identifying the manufacturer or distributor of a product

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

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