Really?
Please name ONE state in which two people cannot meet each other and box FOR FUN, and in which they would be arrested for assault if they did. Cite statutory references.
Technically,
assault is usually legally defined as (illegal)
threat...
battery as any (illegal) "unwanted touching" or "use of force". The two terms frequently get comingled.
More likely, if a fight (without a "victim" claiming the other attacked him against his will) comes into the review of the police, to the problem level of them wanting to actually go through the hassle of an arrest and the subsequent paperwork, they'd charge under common "public order" statutes that can be essentially summarized as
don't be an ahole in public, such as "creating a public disturbance" or "disorderly conduct".