alhamdulilah vs greeting

alhamdulilah and greeting both are nouns.

Word	Noun	Adjective	Verb	Adverb
alhamdulilah	Yes	No	No	No
greeting	Yes	No	No	No

As nouns, greeting is a hypernym of alhamdulilah; that is, greeting is a word with a broader meaning than alhamdulilah:

alhamdulilah: An expression meaning 'praise God' in Arabic
greeting: (usually plural) an acknowledgment or expression of good will (especially on meeting)

Other hypernyms of alhamdulilah include salutation.

alhamdulilah (noun)	greeting (noun)
An expression meaning 'praise God' in Arabic	(usually plural) an acknowledgment or expression of good will (especially on meeting)