Jim Hardy made a big impact with his one plane/two plane golf theory, but I (and others) believe that it is inaccurate. The difference between the two "types" of swings that I've seen are not based on whether or not the club is above the shoulder plane (a rather arbitrary line), but rather how the club is released through impact, and by extension, how the shoulders and hips rotate through impact.
The easiest way to see this distinction is to view the swing down the target line. At some point during the through swing, after impact, the club should be pointing roughly at the target. There are, however, two very different ways to accomplish this.
Below, at 0:17 is Tiger Woods "shaking hands with the target".
Compare to Anthony Kim, at 0:10.
Tiger has his right arm completely extended towards the target and away from his body on the follow through. Anthony Kim, in comparison, has already brought the club so far left and around his body (as opposed to up and away from his body) that it's already hidden from view by the time his right arm extends through to the target.
I believe in TGM (The Golfing Machine) terms, this is referred to as swinging on the TSP (turned shoulder plane) vs. the elbow plane through the impact area. For those who have an interest in what those mean, Brian Manzella's forums and Richie3jack's blog are good places to learn the basics.
This article has a great comparison of Ben Hogan and Tiger Woods from face on which shows the difference between the two "types" of swings.