The center of mass is a point on a body where you can consider all the mass to be concentrated, whereas the center of gravity is a point on a body where you can consider all the WEIGHT to be concentrated.
In any realistic situation, you can treat them both as the center-of-mass.
I've seen center-of-gravity treated as a horizontal location (as on a floor)
which the center-of-mass is directly above or directly below.
In that interpretation & treatment, center-of-mass, being 3d, is more general.