American Dream vs aspiration

American Dream and aspiration both are nouns.

Word	Noun	Adjective	Verb	Adverb
American Dream	Yes	No	No	No
aspiration	Yes	No	No	No

As nouns, aspiration is a hypernym of American Dream; that is, aspiration is a word with a broader meaning than American Dream:

American Dream: the widespread aspiration of Americans to live better than their parents did
aspiration: a cherished desire

Other hypernyms of American Dream include ambition, dream.

American Dream (noun)	aspiration (noun)
the widespread aspiration of Americans to live better than their parents did	the act of inhaling; the drawing in of air (or other gases) as in breathing
	a will to succeed
	a manner of articulation involving an audible release of breath
	a cherished desire