red buckeye vs horse chestnut

red buckeye and horse chestnut both are nouns.

Word	Noun	Adjective	Verb	Adverb
red buckeye	Yes	No	No	No
horse chestnut	Yes	No	No	No

As nouns, horse chestnut is a hypernym of red buckeye; that is, horse chestnut is a word with a broader meaning than red buckeye:

red buckeye: a shrub buckeye of southern United States
horse chestnut: tree having palmate leaves and large clusters of white to red flowers followed by brown shiny inedible seeds

Other hypernyms of red buckeye include Aesculus hippocastanum, buckeye.

red buckeye (noun)	horse chestnut (noun)
a shrub buckeye of southern United States	tree having palmate leaves and large clusters of white to red flowers followed by brown shiny inedible seeds
	the inedible nutlike seed of the horse chestnut