The answer is pretty self-explanatory. Simple assault is when there are either no injuries or very minor injuries. Possibly extremely minor bruising or something along those lines. Battery aggravated assault is when there are injuries, significant bruising, broken bones, cuts, stitches, internal bleeding, things like that will lead to a more aggravated charge, a heightened charge, possibly even a felony. It really depends upon the injuries of the victim when it comes to the definition and classification of the range of assault that the prosecutor is going to charge you with.
