ballpoint vs ballpoint pen

ballpoint and ballpoint pen both are nouns.

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

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

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

Other synonyms of ballpoint include ballpen, Biro.

ballpoint (noun)	ballpoint pen (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