smooth crabgrass vs crab grass

smooth crabgrass and crab grass both are nouns.

Word	Noun	Adjective	Verb	Adverb
smooth crabgrass	Yes	No	No	No
crab grass	Yes	No	No	No

As nouns, crab grass is a hypernym of smooth crabgrass; that is, crab grass is a word with a broader meaning than smooth crabgrass:

smooth crabgrass: a weed, a low-growing, summer annual grass that spreads by seed and from rooting of the lowest joints of the stems (Digitaria ischaemum)
crab grass: grasses with creeping stems that root freely; a pest in lawns

Other hypernyms of smooth crabgrass include crabgrass, finger grass.

smooth crabgrass (noun)	crab grass (noun)
a weed, a low-growing, summer annual grass that spreads by seed and from rooting of the lowest joints of the stems (Digitaria ischaemum)	grasses with creeping stems that root freely; a pest in lawns