ballpoint pen vs ballpoint

ballpoint pen and ballpoint both are nouns.

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

As nouns, ballpoint pen and ballpoint are synonyms defined as:

ballpoint pen and ballpoint: a pen that has a small metal ball as the point of transfer of ink to paper

Other synonyms of ballpoint pen include ballpen, Biro.

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