The dictionary definition of “wet” is a description of the state of an object that is either covered or saturated with water. To be covered with water, the object has to be made of a material that allows water molecules to stay on its surface; to become saturated with water, an object must be made of a material that allows water to enter its pores. For instance, we humans get wet in the rain because water droplets stay on our skin, and a cloth towel gets wet because it absorbs water. A (supposedly) waterproof raincoat may not become wet because it will neither be covered by water nor saturated by it (provided that the raincoat is of high enough quality). A simpler way to state this is that an object only becomes wet if it allows water molecules to stay on or in itself, so simply submerging an object in water may not lead to wetness. In other words, a drop of oil that is being placed into water will not become wet because oil repels water and will not allow water molecules to stay on or in it. Therefore, we see that the submerged object must retain water AFTER being taken out to qualify for the proper definition of wetness.

The definition of wet (from Merriam Webster) is being “covered or saturated with water or another liquid”. This seems like any object that is covered in a liquid would be wet.

If we submerge an object in water, we put the object totally underwater. In order to do this we must necessarily cover the object in water. Thus, while the object is underwater, the object would be wet.

If objects are wet when they come up out of the water, then they are wet when they're under water. Some objects repel water - they're hydrophobic. They probably have a little water in their cracks, if they have them, and on dirty spots on them. Again, they probably are just as wet - or dry - in the water as when they come out of the water.

The word "wet" usually means "covered in water", so yes, they are wet while under water.