vertex coloring graph where no adjacent vertices are similar,
two coloring a graph that you only use 2 colors, and
three coloring a graph that you only use 3 colors

Examples of graphs with colored vertices, that are not graph colorings

Figure N1

Figure N2

Neither of the graphs in figures N1 nor N2 are valid colorings because some adjacent vertices use the same color. That is, two vertices that share an edge have the same color.