The aftershocks occur because the earth has to readjust to the new stress condition produced by the fact that the large earthquake happened.
Aftershocks exhibit a particular pattern with time.
If a small earthquake fits this pattern that is part of this increased earthquake activity following a large event, we call it an aftershock. If it does not fit the pattern, then we say it is just another small earthquake that is part of the natural background rate of earthquake activity. Calling a small earthquake an aftershock simply draws attention that it is related in space or time to the large mainshock. It is based on measuring the amplitude of the seismic waves near 1 Hz or 1 sec period. This means that even though the earthquake is larger, the amplitude near 1-sec period does not significantly change.