What is the difference between a wart and a rash?

Wart is type of rash: A rash is a description for any abnormality of the skin which causes changes in skin color, texture, appearance, thickness, etc. A wart is a type of rash caused by the human papilloma virus, which can occur in almost any area of skin on the body. A wart is a thick raised plaque which is usually not painful, and sometimes goes away on its own.

Totally different: Wart is a type of viral infection of the skin which causes overgrowth of the overlying skin. A rash is a general description, and means any change of the skin from normal, typically related to inflammation or infection.