Here's my take on it

The one plane golf swing is all about connection. Think Vijay. Here the left arm never leaves the chest and the shoulders turn the club back and through. The swing plane is flatter since the arms dont lift the club. This is what Hogan taught in his 5 fundametals I beleive

The 2 plane golf swing is what most pros will teach you nowadays. The swing is initiated by the arms and there is a disconnect between the arms and the chest early in the backswing. The club will stay outside the line of the hands going back and be lifted up into a steeper finish position. On the downswing there has to be a 'move' of some sort to get the club inside the plane and re-connect the arms and chest at impact. David Toms is a good one to look at

I *thiunk* I have a one plane swing. In that I very much try and stay connected and not swing my arms at all. All I try and do is turn my upper body back and through and get width in my takeaway. To me theres far less moving parts this way and the transition move you need in a two plane swing just never worked for me. In fact any time I tried to lead with my lower body in any way (hip bump, knee drive etc) I just could never hit the ball well. One plane means the shoulders just turn the club back and through and I find it much easier

Of couse I could be talking out me preverbial here so hopefuly Greg and Gord etc will correct me