Why ground a plane while fueling?
On cars I think it's because static charges don't build up as much but theoretically it's still possible for a spark to occur when the nozzle touches the tank inlet and provides a ground path.

On airplanes there are two issues:

Static charges built up in the airframe in flight.  For this it is essential to ground the aircraft before the fuel nozzle is brought to the tank inlet.  The risk is of a spark just before the nozzle touches the filler neck, the nozzle itself being grounded, which is right at the location where the air fuel ratio is favourable to ignition. It's also a good idea to touch the nozzle to the fuel cap before you remove it in case the tank isn't adequately bonded to the rest of the airframe, but I don't think anybody does this.

The other one is static charges built up within the fuel tank by the shearing action of the incoming fuel column when adding fuel.  In a large refueling operation, the column of fuel builds huge static charges within the mass of fuel itself, which result in static discharges within the fuel (there are films that show this; a freakin' light show).

Most dangerous is fueling from a plastic can.  When I used to fuel my airplane from cans I made a grounding wire arrangement that bonded the fuel in the can, the fuel tank flange and the ground (using a nail on the end of the wire pushed into the dirt) together.