genus Aster vs aster family

genus Aster and aster family both are nouns.

Word	Noun	Adjective	Verb	Adverb
genus Aster	Yes	No	No	No
aster family	Yes	No	No	No

genus Aster (noun)	aster family (noun)
large genus of herbs widely cultivated for their daisylike flowers	plants with heads composed of many florets: aster, daisy, dandelion, goldenrod, marigold, lettuces, ragweed, sunflower, thistle, zinnia