Trish,
The WCS is one of many vairations of the genre of swing dancing, amongst which are the ECS (single and triple), jive, lindy, shag etc. The characterisitcs that distinguish a WCS from an ECS are these. The ECS as you observed is somewhat rotary although that would be an inexact description. Most figures in the swing start or end with a rock step, such as the change of places (or Underarm turn). The preferred posture is to stand upright or slightly forward (and typical exaggerated stances involve actually bending forward) with your weight over the ball of your feet.
The WCS is what is called a "slot" dance. Imagine one 2x4 (or two) piece of wood on the floor. Typically, the lady (follower) traverses this piece of wood up and down, retaining that slot to do all her figures. The gentleman, or leader, toggles between being on and off this "slot", depending on the figure. There are very few figures where the woman is led to rock back. The posture in the WCS is slightly inclined backwards, like this - \--/ - where the slashes represent the dancers. This gives optimal "connection" between the leader and follower. In other words, the weight is slightly over the heel although not falling backward.
The WCS also has a slinky, sexy kind of attitude to it. The female partner or follower often appears flirtatious and syncopates at will, while the leader's role is to allow her to do what she wishes really. It is a very follower-oriented dance and appears very flamboyant and flirtatious when done correctly.
For a quick primer, visit dancedancedance.com where you will see short video clips of the dance.
Good luck and keep dancing.
