aster family vs genus Aster

aster family and genus Aster both are nouns.

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

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