What is the difference between No Quarter and No Mercy on the battlefield?

No Quarter , means no prisoners, and you keep killing retreating soldiers.

No Mercy means, you leave their wounded laying on the battle field, with no medical treatment.

Ummm...no quarter means you won't give them a place to sleep if you capture any enemy or they surrender to you. Could mean that there are physically no place for them to be interned...battlefield conditions and situations.

No mercy - obviously, this is easy to understand. But if you still don't know, it means you kill the poor basterd. Execution. Pop a cap in, etc.

Technically, if you capture enemy soldiers or they surrender to you, the Geneva Convention requires to house them and feed them. But that's only if you are capable of doing it and have the resources (manpower) to perform such a task.

None. It means no prisoners will be taken.