battle vs wrestle

battle and wrestle both are nouns.

Word	Noun	Adjective	Verb	Adverb
battle	Yes	No	Yes	No
wrestle	Yes	No	Yes	No

As verbs, wrestle is a hyponym of battle; that is, wrestle is a word with a more specific, narrower meaning than battle:

Other hyponyms of battle include dogfight.

battle (noun)	wrestle (noun)
a hostile meeting of opposing military forces in the course of a war	the act of engaging in close hand-to-hand combat
an energetic attempt to achieve something
an open clash between two opposing groups (or individuals)

battle (verb)	wrestle (verb)
battle or contend against in or as if in a battle	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)