Wrong. Technically speaking, assault is any illegal contact with another person, meaning any unwelcome contact. Battery is the same thing but with the intent to inflict harm on the other person.
In my previous post, I meant to say battery is threatening or intending harm and assault is just harming another person.
To be more clear, if you get in a fight with someone and just try to defend yourself, that's assault. But if you get in a fight and try to break the other person's nose just to cause them pain, that's battery.
Battery is the more serious offense, unless the charge is aggravated assault.