pen vs ballpen

pen and ballpen both are nouns.

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

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

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

pen (noun)	ballpen (noun)
female swan	a pen that has a small metal ball as the point of transfer of ink to paper
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

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