Just to add a bit more confusion to the pot, what is known as "assault in Florida, is called "menacing" in New York. These two statutes deal with a threat of physical violence instead of actual physical violence, while Assault in New York and Battery in Florida deal, respectively, with actual physical violence inflicted on another.
But the differences do not stop with the nomenclature. In Florida, for a "Battery," all that needs to occur is that someone touched another person against that person's will. There is no need for physical injury or even an intent to cause physical injury. That conduct in Florida is a 1st degree misdemeanor punishable by up to 1 year in jail.
In New York, actual physical injury is required. Otherwise, the behavior falls short of an "assault" but may be punishable as an attempted assault, which is a "B" misdemeanor with a maximum penalty of 90 days jail. Or, if no intent to cause physical injury can be proven but there is physical conduct which is at least annoying. the charge can be an Harassment under Penal LAw 240.26 which is just a violation with a maximum penalty of 15 days jail.
Both states have codified the common law right to self-defense in that both states find that a person can use physical force when that person reasonably believes that such conduct is necessary to defend himself or herself or another against the other’s imminent use of unlawful force.
But New York's self defense laws might be more limited than Florida's. One example of the difference is that, in New York, physical force which cause injury is not excusable as the product of combat by mutual agreement unless it is specifically authorized by law. That is cited in some New York cases and even in the New York jury instructions on self defense. But in Florida, it seems that mutual combat as a defense is still viable under some circumstances. In any event, check with your lawyer.
One good way to understand a statute is to compare it with the Statute of another State. Florida's Misdmeanor Battery Statute provides a nice comparison/contrast to New York's Assault Statute. I used to practice in Florida and between New York and Florida I have handled plenty of cases where someone got charged with inflicting physical injury on another. At the misdemeanor level, New York calls this type of behavior "Assault" while in Florida it is called "Battery".