The sling is meant to hold up the legs and make it easier for the partner, who is receiving, to tilt their pelvis (while in the standing missionary position) in a direction that is pleasant to him or her. While it is usually used to loosely bind the ankles to a strap that is slung around the giving partner's head and shoulders. Does this make any sense?
The swing is different. The swing is just a good time for everyone invited . With the swing, the person in the swing can do or have done to them all sorts of fun stuff. For example, lets say the female is in the swing, she can sit in the swing and have cunnilingus performed on her while she is sitting or she can swing onto his erection (not recommended). Pretty much, with the swing, you have many more options, however, it will take up much more space.