Water is made up of hydrogen and oxygen. While underwater the water molecules glide and some stick to your body but they do not break off of your body until they are subjected to air which gives you the "wet" sensation.
So in other words if I am above water and spill some water on my arm then I am wet because it is interacting with the oxygen in the air. If my arm is underwater then it is not wet because it is constantly underwater and the water molecules are just gliding along my skin and it isn't until my arm is removed from the water that is becomes attached to my arm and makes it feel wet.
Water = wet when above water but when submerged in water then water doesn't necessarily equal wet.