Felony battery is a battery that results in great bodily harm. Let's take your hypothetical example but put a twist on it. If a cashier angers you and you punch them, then you are correct it's a misdemeanor battery. Let's say that when you punch the cashier, you break his/her nose or knock out a tooth or give them a scar. Then you have a misdemeanor battery but the injuries upgrade it to a Felony Battery.
Aggravated Battery (without a weapon) is a lot like Felony Battery. There is a battery and there is great bodily harm. The difference is that with an Aggravated Battery there is the Intent to cause the great bodily harm. So again with your hypothetical, if you punched the cashier and specifically intended to cause the broken nose/broken tooth/scar, and actually caused it, then there is an Aggravated Battery.
Both Felony Battery and Aggravated Battery have great bodily harm, which separate them from misdemeanor battery, but the difference between Felony Battery and Aggravated Battery is the Intent.
Feel free to email me if you'd like to discuss this further.
The prior post is an excellent outline but another justification for misdemeanor battery becoming felony battery is if you have a prior battery conviction. A second battery can be elevated to a felony even if it would otherwise be a misdemeanor. If the cashier was a family or household member or was a person with whom you are in a dating relationship with and you strangled him/her that could be a felony as well on the first offense.
I concur with the prior advice. I can only add this pearl of wisdom: if the cashier upsets you, speak to his manager, dont hit him in the face. That's the best way to keep your question a hypothetical one
Robert E. Heyman, Esq