trademark vs logotype

trademark and logotype both are nouns.

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

As nouns, logotype is a hyponym of trademark; that is, logotype is a word with a more specific, narrower meaning than trademark:

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

Other hyponyms of trademark include Sharpie, logo.

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

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