gumshoe vs police detective

gumshoe and police detective both are nouns.

Word	Noun	Adjective	Verb	Adverb
gumshoe	Yes	No	No	No
police detective	Yes	No	No	No

As nouns, police detective is a hypernym of gumshoe; that is, police detective is a word with a broader meaning than gumshoe:

Other hypernyms of gumshoe include detective, investigator, tec.

gumshoe (noun)	police detective (noun)
a waterproof overshoe that protects shoes from water or snow	a police officer who investigates crimes
someone who is a detective