  More than ten years ago in 2008, a new kind of graph coloring appeared in
graph theory, which is the {\it rainbow connection coloring} of graphs, and
then followed by some other new concepts of graph colorings, such as {\it
proper connection coloring, monochromatic connection coloring, and
conflict-free connection coloring} of graphs. In about ten years of our
consistent study, we found that these new concepts of graph colorings are
actually quite different from the classic graph colorings. These {\it colored
connection colorings} of graphs are brand-new colorings and they need to take
care of global structural properties (for example, connectivity) of a graph
under the colorings; while the traditional colorings of graphs are colorings
under which only local structural properties (adjacent vertices or edges) of a
graph are taken care of. Both classic colorings and the new colored connection
colorings can produce the so-called chromatic numbers. We call the colored
connection numbers the {\it global chromatic numbers}, and the classic or
traditional chromatic numbers the {\it local chromatic numbers}. This paper
intends to clarify the difference between the colored connection colorings and
the traditional colorings, and finally to propose the new concepts of global
colorings under which global structural properties of the colored graph are
kept, and the global chromatic numbers.
