The difference between Barycentre and Centre of mass

Barycentre as a noun (mathematics, physics, astronomy):

The point at the centre of a system; an average point, weighted according to mass or other attribute. The term is usually used in astronomy for the centre of mass about which a system rotates, for example, the moon and the earth rotate about a common point within the earth but not near the centre. Jupiter and the Sun rotate about a common point just outside the surface of the Sun.

Centre of mass as a noun (mathematics, physics):

A point, near, or within a body at which the object's mass can be assumed to be concentrated; it coincides with the centroid for a body of uniform density, and with the centre of gravity in a uniform gravitational field.