I think the terms SAW (squad automatic weapon) and light support weapon are interchangeable. The American Army calls their weapon the SAW and the British Army calls theirs the LSW. Both terms refer to a light automatic weapon employed at the squad or fire team level. These weapons are usually chambered in the same caliber as the rifle the rest of the squad uses.
They are used mostly to provide the base of fire to pin the enemy down while the rest of the squad maneuvers on the enemy.
I don't see the utility of optics on a weapon of this type. They are not precision weapons. Their value is in their ability to put out a lot of sustained fire to keep the enemy's head down while the rest of the squad or team maneuvers to a position from which to attack from. Belt fed weapons are best in this role. No breaks in fire while you change magazines.
Perhaps you are referring to the GP (general purpose)machine gun when you ask about the difference. The GP machine gun (M60, M240, MAG 58, RPD) is employed at the platoon level, is normally chambered in a full caliber (7.62x51). Normally a platoon will have two or three GP machineguns in most current organizations. These are crew served weapons (SAWs and LSWs are individual weapons)and normally employed from tripod mounts. They are used to form the base of fire upon which the platoon maneuvers.