Yes, sandpaper can be used both wet and dry, depending on the type and the application. 
Dry sandpaper is typically used for general sanding tasks on wood, metal, and other materials. It is effective for removing material quickly and is often used in initial sanding stages. However, it can produce a lot of dust, which may require protective measures such as masks and goggles.
Wet sandpaper, also known as wet/dry sandpaper, is designed to be used with water or other lubricants. The water acts as a lubricant, reducing friction and preventing the sandpaper from clogging with dust. This method is particularly useful for fine sanding and finishing tasks, as it provides a smoother finish and reduces the risk of scratching the surface. Wet sanding is commonly used in automotive refinishing, woodworking, and metalworking to achieve a high-gloss finish.
When using sandpaper wet, it is important to ensure that the sandpaper is specifically labeled for wet use, as not all sandpapers are suitable for this method. Wet/dry sandpaper is typically made with a waterproof backing and abrasive materials that can withstand moisture.
In summary, the choice between wet and dry sandpaper depends on the specific requirements of the task, the material being sanded, and the desired finish.