Settling time (tS) is the time it takes for an op-amp to settle to achieve the specified accuracy at the output (i.e., 10%, 1%, 0.1%, etc ). It is strongly dependent on the circuit components in the signal and feedback paths (resistors, capacitors, inductors) and the PCB layout.
Overshoot is the amount of the output voltage exceeds its target value, in %. The percentage overshoot is the maximum value minus the step value divided by the step value. The picture below shows the step response of VOUT with regard to overshoot and settling time.