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UV filters are used to reduce haziness created by ultraviolet light. A UV filter is mostly transparent to visible light, and can be left on the lens for nearly all shots. UV filters are often used for lens protection, much like clear filters.
Clear filters, also known as window glass filters or optical flats, are completely transparent, and (ideally) perform no filtering of incoming light at all. The only use of a clear filter is to protect the front of a lens.