doughnut fryer vs frier

doughnut fryer and frier both are nouns.

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

As nouns, frier is a hypernym of doughnut fryer; that is, frier is a word with a broader meaning than doughnut fryer:

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

Other hypernyms of doughnut fryer include machine, deep fat fryer, deep fryer, fryer, fryolator.

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