ballpoint pen vs pen

ballpoint pen and pen both are nouns.

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

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

ballpoint pen: 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

ballpoint pen (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

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