In my experience, jog can mean at least two different things.
First, it can mean that there is a separate jog button that, when pushed causes the motor to run, and when released, causes the motor to stop. Operation is completely independent of the start and stop buttons.
Second, it can mean that there is a two position selector switch which, in run position, causes the start button to latch up leaving the motor running until the stop button is pushed. In jog position on the switch, the start button causes the motor to run when pushed and does not latch up, allowing the motor to stop when released.
The control scheme for these is significantly different.