Pull off (a car) / pull out (a car) | WordReferenc...

Context is important. Clearly if the van is moving it can't start moving!

To me, to pull over means to move to the nearside of the road that you have been travelling on and stopping but without actually leaving the road.
To pull off the road you are on, you move off the road altogether and into a neighbouring area where you can drive or stop or park.
To pull up means to stop, e.g. at traffic lights.
To pull out means that you are driving along and move into another lane. For example to overtake another vehicle.
To pull in usually refers to going into a petrol station or similar.

Good luck with English prepositions!!!!

The police officer signalled for her to pull over. She moved to the near lane and switched off the engine.

The car had a flat tyre. John pulled off the road so that he wouldn't be in the way of traffic.

Kate was driving home when a child ran into the road. Kate had to pull up very quickly.

The Formula 1 driver pulled out so that he could overtake. Unfortunately he pulled out in front of a third car and they both spun off the track.

Jane felt hungry so she pulled in at a roadside cafe.