chess piece vs chessman

chess piece and chessman both are nouns.

Word	Noun	Adjective	Verb	Adverb
chess piece	Yes	No	No	No
chessman	Yes	No	No	No

As nouns, chess piece and chessman are synonyms defined as:

chess piece and chessman: any of 16 white and 16 black pieces used in playing the game of chess

chess piece (noun)	chessman (noun)
any of 16 white and 16 black pieces used in playing the game of chess	any of 16 white and 16 black pieces used in playing the game of chess