A polygon in a computer graphics (image generation) system is a two-dimensional shape that is modelled and stored within its database. A polygon can be colored, shaded and textured, and its position in the database is defined by the coordinates of its vertices (corners).
A vertex (plural vertices) in computer graphics is a data structure that describes a point in 2D or 3D space. Display objects are composed of arrays of flat surfaces (typically triangles) and vertices define the location and other attributes of the corners of the surfaces.