PS. I looked it up. In jurisdictions (such as South Africa) where assault is defined as "any physical contact without consent" - there is no such crime as battery, as the definition of assault already encompasses all the actions that, in other jurisdictions, would be battery.

In jurisdictions that separate them: assault is the act of threatening to harm somebody, battery is actually touching them in a way intended to cause offense, harm or threat. So you generally cannot commit battery without first committing assault, but you could commit assault without also committing battery (trying to punch somebody and missing).