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 Slingbacks:
Slingbacks are a type in shoe in which the heel is exposed yet is contained or secured by a strap that sits above the heel around the ankle.