Raising your fist at someone isn't assault. I'm no lawyer or police officer, but I doubt anyone, ever, has been arrested or charged for raising their fist at someone.
You're incorrect.
Overview of Florida Assault and Battery Laws
Although assault and battery are often related crimes and discussed together, the two are actually distinct offenses. Florida state laws define the two crimes separately.
Assault refers to a threat of harm that leads to the victim's fear of imminent harm. The offense
does not include physical contact between the perpetrator and the victim. First a prosecutor must show that the defendant intended to threaten the victim, cause the victim to feel fear,
or carry out a violent act. A defendant may want try to show a lack of criminal intent claiming the act was an accident or a joke. The prosecutor must also show that the defendant demonstrated the threat through words, a gesture, or an intimidating act. The defendant must have shown an ability to carry out the threat and the victim must have feared imminent harm.
Florida statutes establish specific offenses for simple assault, aggravated assault, and felony assault. The severity of the offense and the potential punishment depends on the type of assault charged by the state prosecutor.
When the defendant makes physical contact with the victim, Florida state laws allow for prosecution of the act as a battery. To prove a battery case, the prosecutor must show that the defendant intentionally touched or struck the victim. The physical contact must have been against the victim's will and done without the victim's consent.
As with assault, Florida law establishes several types of battery. Simple battery only requires an intentional, unwanted physical contact between the defendant and the victim. If the defendant has a previous conviction for battery, state laws permit the prosecutor to charge the defendant with felony battery for a subsequent offense. To prove aggravated battery, the prosecutor must show that the defendant intended to cause serious bodily injury to the victim or that the defendant used a deadly weapon.