As mentioned there are different types of hitches, weight carrying and weight distribution, as well sway controls. Sway control can be used on either type of hitch. The type hitch you use is relative to the size/weight of the trailer, although you can use the weight distributing type for most any pull trailer, the weight carrying type is limited as the trailer weight increases.  Normally, once you go beyond 5000lb or 500lb tongue weight you need the weight distributing hitch. This shows the  'hitch receiver' which also has different classes for weight applications.

"On your receiver hitch or hitch receiver, you will usually see the tag with classifications for maximum tongue weight and maximum trailer weight. The lower weight is for WC which is "Weight Carrying" hitch or drawbar/stinger. In this situation all the tongue weight is on the WC hitch, draw bar. The other classification on the tag found on your towing vehicle's receiver hitch is the higher weight carrying capacity for WD which is the "Weight Distributing" hitch that spreads out the tongue weight of the trailer. An important note here is that most vehicle manufactures will only allow a maximum trailer capacity of 5000#'s and 500#'s of tongue weight without using a weight distributing hitch."

The WDH is designed to "distribute the trailer weight evenly to all axles of the truck/SUV and trailer, which in turn gives you better control of the vehicle and trailer.   These are actually required for maximum towing by most manufactures and when you go over the 5000 lb towing weight. "