calling card vs greeting

calling card and greeting both are nouns.

Word	Noun	Adjective	Verb	Adverb
calling card	Yes	No	No	No
greeting	Yes	No	No	No

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

calling card: a printed or written greeting that is left to indicate that you have visited
greeting: (usually plural) an acknowledgment or expression of good will (especially on meeting)

Other hypernyms of calling card include salutation.

calling card (noun)	greeting (noun)
a distinguishing characteristic or behavior	(usually plural) an acknowledgment or expression of good will (especially on meeting)
a printed or written greeting that is left to indicate that you have visited
a card that is used instead of cash to make telephone calls