dog grass vs wheatgrass

dog grass and wheatgrass both are nouns.

Word	Noun	Adjective	Verb	Adverb
dog grass	Yes	No	No	No
wheatgrass	Yes	No	No	No

As nouns, wheatgrass is a hypernym of dog grass; that is, wheatgrass is a word with a broader meaning than dog grass:

dog grass: European grass spreading rapidly by creeping rhizomes; naturalized in North America as a weed
wheatgrass: a grass of the genus Agropyron

Other hypernyms of dog grass include wheat-grass.

dog grass (noun)	wheatgrass (noun)
European grass spreading rapidly by creeping rhizomes; naturalized in North America as a weed	a grass of the genus Agropyron