These two terms are very close in meaning and can almost be used synonymously.  Both terms refer to reenforced concrete used as a foundational support for a structure.  A grade beam is found closer to the surface and is typically not located below the frost line. It can be part of a monolithic pour which means it is poured within the same forms, and at the same time, as the floor.  A footing can be any type of reenforced beam or pad used for structural support.  One way to look at it is, a grade beam is a footing, but a footing is not necessarily a grade beam.