ballpen vs pen

ballpen and pen both are nouns.

Word	Noun	Adjective	Verb	Adverb
ballpen	Yes	No	No	No
pen	Yes	No	Yes	No

As nouns, pen is a hypernym of ballpen; that is, pen is a word with a broader meaning than ballpen:

ballpen: a pen that has a small metal ball as the point of transfer of ink to paper
pen: a writing implement with a point from which ink flows

ballpen (noun)	pen (noun)
a pen that has a small metal ball as the point of transfer of ink to paper	female swan
	a writing implement with a point from which ink flows
	an enclosure for confining livestock
	a correctional institution for those convicted of major crimes
	a portable enclosure in which babies may be left to play

ballpen (verb)	pen (verb)
	produce a literary work