chessman vs chess piece

chessman and chess piece both are nouns.

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

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

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

chessman (noun)	chess piece (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