Arch Support generally refers to the part of the insole of the shoe that raises right at the level of the arch to provide support to the midfoot. Arch Support also refers to individual insole cups with a molded shape that fit the arch and are placed inside the shoe to help relieve foot or heel pain.
About Slippers:
A type of shoe typically designed for indoor use that can be a variety of styles, including slides, mocassins, scuffs, booties, thongs, or loafers. Usually the uppers are made of soft leather or other fabrics (as opposed to tougher fabrics like hard leather that regular shoes are made of) and are sometimes lined with soft materials like felt, shearling or wool.