green June beetle vs May beetle

green June beetle and May beetle both are nouns.

Word	Noun	Adjective	Verb	Adverb
green June beetle	Yes	No	No	No
May beetle	Yes	No	No	No

As nouns, May beetle is a hypernym of green June beetle; that is, May beetle is a word with a broader meaning than green June beetle:

green June beetle: large greenish June beetle of southern United States
May beetle: any of various large usually brown North American leaf-eating beetles common in late spring; the larvae feed on roots of grasses etc.

Other hypernyms of green June beetle include June beetle, June bug, May bug.

green June beetle (noun)	May beetle (noun)
large greenish June beetle of southern United States	any of various large European beetles destructive to vegetation as both larvae and adult
	any of various large usually brown North American leaf-eating beetles common in late spring; the larvae feed on roots of grasses etc.