Tessellations of the plane can be classified as follows:
Regular Tesselations are comprised of simple repetitions of the same regular polygon. There are three distinct regular tessellations: equilateral triangles, squares and hexagons.
Semiregular Tessellations are comprised of repetitions of two or more regular polygons, where the number and type of each kind of polygon surrounding each vertex is the same for all vertices in the plane. There are eight such semiregular tessellations. These are often referred to as Archimedean tessellations.
Demiregular Tessellations are comprised of repetitions of two or more regular polygons, where the number and type of each kind of polygon surrounding each vertex is different for some of the vertices in the plane. Although it can be argued that the number of such tessellations is infinite, they can be reduced to 14 specific types.
Other tessellations of the plane exist. See for example the tilings of M.C. Escher, such as the one which is illustrated here. Such tilings are not tessellations, in that they are not comprised of polygons. However, these tilings are based on one of the above named types of tessellation.
The tiling illustrated is based on a regular tessellation of squares.