trooper vs lancer

trooper and lancer both are nouns.

Word	Noun	Adjective	Verb	Adverb
trooper	Yes	No	No	No
lancer	Yes	No	No	No

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

Other hyponyms of trooper include cuirassier, dragoon, hussar, Rough Rider.

trooper (noun)	lancer (noun)
a mounted police officer	(formerly) a cavalryman armed with a lance
a soldier in a motorized army unit
a state police officer
a soldier mounted on horseback