The caliper has to come off to the check their movement.
You will see a rubber boot on both sides.
This boot is one peice and goes through the caliper casting.
The pin floats inside the rubber on moulded in suspension projections such that the pin is sealed from water unless the boot has torn or opens in some manner.
The pin is dry (no lube) inside.
The pin can't actually set fast in rubber unless rust and dirt build up inside.
The caliper has to move [on the pin] to conform to the changes in thickness of the pads as they wear and be able to move in general with changes in disc thickness and minor warping over time and movement.
Good luck.