check out vs follow up on

check out and follow up on both are verbs.

Word	Noun	Adjective	Verb	Adverb
check out	No	No	Yes	No
follow up on	No	No	Yes	No

As verbs, follow up on is a hypernym of check out; that is, follow up on is a word with a broader meaning than check out:

Other hypernyms of check out include act on, pursue.

check out (verb)	follow up on (verb)
examine so as to determine accuracy, quality, or condition	carry further or advance
announce one's departure from a hotel
try to learn someone's opinions and intentions
record, add up, and receive payment for items purchased
withdraw money by writing a check
trace
be verified or confirmed; pass inspection