Known as "Assault" or "Assault and Battery" in some other states, "Battery" in Florida is where there is the intentional touching or striking of another person against that person's will or when there is the intentional causing of bodily harm to another person.
Battery (Florida Statute 784.03) is not a crime unless it is intentional/willful/purposeful. If you poke, kick, slap, push, chop, punch, etc. another person, you may still be arrested, but odds are good you would not be charged, and if indeed charged, your case would be dropped by the prosecutor's office or you would be found not guilty at trial. Most prosecutors are fair, especially after having listened to reason, and most juries are fair. Battery is also known as "misdemeanor battery" or "simple battery." If the battery is against a law enforcement officer or a handful of other professions who routinely work with the public, it is a 3rd degree felony. Same goes for if the battery is against one 65 years of age or older and certain types of batteries against children. Otherwise, it is a 1st degree misdemeanor punishable by up to 1 year in jail, which very rarely occurs.
Felony Battery (784.041) is when the intentional touching or striking of a person against that person's will causes something unintended: great bodily harm, permanent disability, or permanent disfigurement. Of the three, of course "great bodily harm" is the most prevalent in arrests and filed cases, and the prosecutor's office has discretion as to what "great bodily harm" entails. One typically need not look beyond its plain meaning. Felony Battery has been a crime for less than a generation and is a 3rd degree felony punishable by up to 5 years in prison, which very rarely occurs.
Aggravated Battery (784.045) is Felony Battery, but the end result was intentional. It can also involve battery with the use of a deadly weapon or when the battery victim is pregnant and the offender knew or should have known the victim was pregnant. It is a 2nd degre felony punishable by up to 15 years in prison, which very rarely occurs.
Battery - Offender intentionally pushes victim against victim's will.
Felony Battery - Offender intentionally pushes victim against victim's will, unintentionally causing great bodily harm (broken arm and/or something else beyond mere "bodily harm").
Aggravated Battery - Offender intentionally pushes victim against victim's will, intentionally causing great bodily harm.
Cases are dropped, defendants prevail at trial, and for those who plea, sometimes the plea is to something lesser, like Felony Battery instead of Aggravated Battery, or Battery instead of Felony Battery. The one thing that ties the three together is that the crime must have been committed intentionally.