how-do-you-do vs greeting

how-do-you-do and greeting both are nouns.

Word	Noun	Adjective	Verb	Adverb
how-do-you-do	Yes	No	No	No
greeting	Yes	No	No	No

As nouns, greeting is a hypernym of how-do-you-do; that is, greeting is a word with a broader meaning than how-do-you-do:

how-do-you-do: an expression of greeting
greeting: (usually plural) an acknowledgment or expression of good will (especially on meeting)

Other hypernyms of how-do-you-do include salutation.

how-do-you-do (noun)	greeting (noun)
an expression of greeting	(usually plural) an acknowledgment or expression of good will (especially on meeting)
an awkward situation