hugger-mugger vs topsy-turvy

hugger-mugger is a noun but topsy-turvy is not a noun.

Word	Noun	Adjective	Verb	Adverb
hugger-mugger	Yes	Yes	No	Yes
topsy-turvy	No	Yes	No	Yes

As adjectives, hugger-mugger and topsy-turvy are synonyms defined as:

Other synonyms of hugger-mugger include disorderly, higgledy-piggledy, jumbled.

hugger-mugger (noun)	topsy-turvy (noun)
a state of confusion

hugger-mugger (adjective)	topsy-turvy (adjective)
conducted with or marked by hidden aims or methods	in utter disorder
in utter disorder

hugger-mugger (adverb)	topsy-turvy (adverb)
in secrecy	in disorderly haste
	in a disordered manner