They are the different names for the same concept.
The “center of gravity” is the “center of mass” when dealing with a gravitational force on an object (mass).
When dealing with the forces in the universe, the impact of the mass of an object is physically and mathematically focused on the “center of mass”. For mass, that will NOT often be the geometric center of an object! Thus, it is very import to identify and locate the “center of mass” in order to correctly solve problems related to its interactions with other masses and forces.