The can both be used interchangeably if you are talking about traversing a distance. But if you are talking about continuing an action, even if that action is actually mobile, like running, then you would use "keep going" rather than move on.

No, they're not completely the same. They both mean to continue or move forward, but "move on" can mean to recuperate from a loss. "I know your girlfriend left you, but you need to learn to move on." "After I lost my mom, it was really difficult to move on with my life." That's really the only small difference I know of between move on and keep going.