mud-wrestle vs wrestle

mud-wrestle is not a noun while wrestle is a noun.

Word	Noun	Adjective	Verb	Adverb
mud-wrestle	No	No	Yes	No
wrestle	Yes	No	Yes	No

As verbs, wrestle is a hypernym of mud-wrestle; that is, wrestle is a word with a broader meaning than mud-wrestle:

mud-wrestle (noun)	wrestle (noun)
	the act of engaging in close hand-to-hand combat

mud-wrestle (verb)	wrestle (verb)
wrestle in mud	engage in deep thought, consideration, or debate
	combat to overcome an opposing tendency or force
	engage in a wrestling match
	to move in a twisting or contorted motion, (especially when struggling)