frier vs doughnut fryer

frier and doughnut fryer both are nouns.

Word	Noun	Adjective	Verb	Adverb
frier	Yes	No	No	No
doughnut fryer	Yes	No	No	No

As nouns, doughnut fryer is a hyponym of frier; that is, doughnut fryer is a word with a more specific, narrower meaning than frier:

frier: A kitchen appliance for deep frying; its size depends on intended use.
doughnut fryer: a machine used to fry large quantities of doughnuts at once.

Other hyponyms of frier include donut fryer, donut machine, doughnut machine.

frier (noun)	doughnut fryer (noun)
A kitchen appliance for deep frying; its size depends on intended use.	a machine used to fry large quantities of doughnuts at once.
flesh of a medium-sized young chicken suitable for frying