counterspy vs undercover agent

counterspy and undercover agent both are nouns.

Word	Noun	Adjective	Verb	Adverb
counterspy	Yes	No	No	No
undercover agent	Yes	No	No	No

As nouns, undercover agent is a hypernym of counterspy; that is, undercover agent is a word with a broader meaning than counterspy:

counterspy: a spy who works against enemy espionage
undercover agent: (military) a secret agent hired by a state to obtain information about its enemies or by a business to obtain industrial secrets from competitors

Other hypernyms of counterspy include spy.

counterspy (noun)	undercover agent (noun)
a spy who works against enemy espionage	(military) a secret agent hired by a state to obtain information about its enemies or by a business to obtain industrial secrets from competitors