make merry vs fete

make merry is not a noun while fete is a noun.

Word	Noun	Adjective	Verb	Adverb
make merry	No	No	Yes	No
fete	Yes	No	Yes	No

As verbs, fete is a hypernym of make merry; that is, fete is a word with a broader meaning than make merry:

make merry: celebrate noisily, often indulging in drinking; engage in uproarious festivities
fete: have a celebration

Other hypernyms of make merry include celebrate.

make merry (noun)	fete (noun)
	an organized series of acts and performances (usually in one place)
	an elaborate party (often outdoors)

make merry (verb)	fete (verb)
celebrate noisily, often indulging in drinking; engage in uproarious festivities	have a celebration