ballpen vs ballpoint pen

ballpen and ballpoint pen both are nouns.

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

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

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

Other synonyms of ballpen include ballpoint, Biro.

ballpen (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