A vector graphic is an artwork made up of points, lines, and curves based upon mathematical equations, rather than on solid-colored square pixels as in raster images.
Vector graphics are used to create graphics that need to be scaled. The nature of vector graphics ensures that images can be scaled down for a business card or up for a billboard.
Vector artwork refers to any art made with vector illustration software. Vector artwork is built from vector graphics, which are images created with mathematical formulas.