I'll try to make it simple...
Engine running and warm:
Piston and cylinder and coolant are fairly close to the same temperature.
Coolant removing heat from cylinder and piston. Coolant temp 123*
Engine shuts off:
Piston and cylinder are still fairly close to the same temp however now the coolant is not removing heat at the same rate because it is not flowing. Coolant temp rises to lets say 170*. At this time the coolant in the coolers is cooling rapidly, lets say to 65*
Engine fires back up:
Piston and cylinder are relatively close to the same temperature but quite high. Water pump starts flowing coolant. Thermostat is still open allowing hot coolant to escape and cold coolant to enter around the cylinder. Thermostat senses colder coolant and starts to close. At this time the colder coolant cools off the cylinder, but not the piston. Piston is still hot and therefore expanded. Cylinder walls get colder from the colder coolant flowing in thus contracting. This occurs rather quickly and since the thermostat is closed the coolant starts heating up as combustion warms the cylinder.
This is the cold shot.
The cold seize is when everything is cool. Engine fires up. Joe Schmuck nails the throttle across the parking lot. Piston heats up way faster than the cylinder and sticks the piston. Joe drags his sled back to the truck. If he is lucky (not really), after everything cools down, he might be able to pull the rope and turn the engine over. Won't do him much good unless he has one of those old motors that are very forgiving. Haha