"Domestic violence" in this context has to do with the relationship between the defendant and victim, not the label on the misdemeanor.
It’s a federal crime for someone convicted of a domestic violence offense to possess a firearm. In 2014, the U.S. Supreme Court decided that “domestic violence” in this context doesn’t necessarily involve “violence.” (See What kind of “domestic violence” conviction prevents you from having a gun?)
Five years earlier, the Court decided a slightly different issue. It determined that misdemeanors that don’t have the “domestic violence” label can nevertheless qualify as domestic violence for gun possession purposes. In a 2009 case, the Court reviewed a man’s federal conviction for possessing a firearm after having been convicted of a misdemeanor crime of domestic violence. Officers had found a rifle in the defendant’s home when responding to a 911 call. Ten years earlier, he had been convicted, under West Virginia law, of battery against his then-wife. The battery conviction didn’t involve “domestic violence” in that the relevant statute applied to all sorts of people, not just those in domestic relationships. The law applied to anyone who “unlawfully and intentionally makes physical contact of an insulting or provoking nature with the person of another or unlawfully and intentionally causes physical harm to another person….”
The defense argued that the battery conviction didn’t qualify as domestic violence. It pointed to the fact that the battery statute didn’t specify the existence of a domestic relationship between a defendant and victim. But the Supreme Court held that, in order to qualify as a domestic violence misdemeanor for purposes of the federal gun possession law, the prior offense doesn’t need a "domestic relationship" element. The Court decided that what matters is not whether the law mentions a domestic relationship, but whether the offender and victim actually had such a relationship. In other words, the defendant’s conviction for plain old battery could qualify as domestic violence. (United States v. Hayes, 555 U.S. 415 (2009).)