chess composition vs mystifier

chess composition and mystifier both are nouns.

Word	Noun	Adjective	Verb	Adverb
chess composition	Yes	No	No	No
mystifier	Yes	No	No	No

As nouns, mystifier is a hypernym of chess composition; that is, mystifier is a word with a broader meaning than chess composition:

chess composition: a puzzle set by somebody using chess pieces on a chess board, that presents the solver with a particular task to be achieved.
mystifier: a particularly baffling problem that is said to have a correct solution

Other hypernyms of chess composition include puzzle, puzzler, teaser.

chess composition (noun)	mystifier (noun)
the process of composing (and solving) chess problems.	a particularly baffling problem that is said to have a correct solution
a puzzle set by somebody using chess pieces on a chess board, that presents the solver with a particular task to be achieved.