Firstly you should not try to 'drive' a stuck motor, if a motor is stuck shut the motors down ASAP by holding the throttle closed.
Rather you should remove the grass and try to turn the motor by hand to test whether can be turned freely, as freely as the others.
Why? A stuck motor is effectively a short circuit.
Unless the control circuits are designed to handle such an event, i.e. probably cut the power, the current may be such that it can cook the ESC.
This was, I believe, a problem with the Phantom 3 and I have had an ESC warning with a Phantom 3 that flipped and briefly stalled a motor, fortunately I had engaged the CSC stick position as soon as it flipped and shut off the motors quickly. The warning disappeared once things had cooled down.
The use of the CSC with a Mavic is 'problematic' and the subject for a different discussion, hence my saying hold the throttle closed.
If you have cooked the relevant ESC then it will need to be replaced. I do not remember if the ESC's are on a separate board. If they are not and are on the main board you likely face having to replace the main board, probably expensive.
Removing and replacing an ESC is likely to be beyond the capabilities of a DIY'er so even if the ESCs are on a separate board a cooked ESC likely means you will have to replace that board.
To answer you "are the motors the same" question, I believe the actual motors are the same ..... but the front and rear wiring looms incorporated with the motors differ since the front looms also contain the antennae wiring.
You can, I believe, swap left and right motor and their looms but it may be tricky to get the loom and its sleeving of the 'new motor' through the old arm, it may be easier to swap a complete arm and motor assembly, in which case there is no need to worry about the interchangeability of the motors. If you do that KEEP the old arm, its a useful spare, also watch several dismantling videos as the rear arms need to be in a certain position to remove them from the drone and to refit them.
I haven't looked to see how easily the wiring loom could removed and reattached from the actual motor but the loom is fairly easy to disconnect and reconnect from the control board in the drone, a decent soldering iron will do that. I had to rebuild a crashed
M2Z.
I would however attempt to ascertain whether you have in fact cooked the ESC before you go looking for a new motor.
Check the motor itself to see if the varnish/insulation on the motor windings appears burnt. If not and if you can un-jam the motor and get it turning freely then see if you still get an ESC warning. I do not know if it will be detected during the boot but suspect it might be.
If a burnt ESC/stuck motor is not detected during the boot and it is necessary to try to start the motors (use the CSC position) be prepared to stop the motors ASAP by holding the throttle shut if all the motors do not start.