green June beetle vs May bug

green June beetle and May bug both are nouns.

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

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

green June beetle: large greenish June beetle of southern United States
May bug: 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 beetle.

green June beetle (noun)	May bug (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.