What is the difference between Xbox 360 and a Xbox 360S?

The Xbox 360 hardware has gone through 3 major revisions:

Here's a photo from a CNet review of the E:

The one on the left is the "old style" Xbox 360. There were a couple of versions of this, and some early models did not come with HDMI ports. You're only going to buy one of these if you buy used, and I'd be careful. A lot of the early run had issues with overheating and were prone to the "red ring of death."

The middle unit is the Xbox 360 S. It improves on the classic 360 by adding a dedicated Kinect port, additional USB ports, integrated wireless and a built-in optical audio out. All of these models come with HDMI ports.

The one on the right is the Xbox 360 E. It is a redesign of the 360 S to make it look a bit more like the Xbox One. However, they dropped the optical out, the AV port (for Component video) and a USB port. There's no real advantage to this model as far as I can see. (The linked CNet review says the pros are it's "slightly quieter")

In addition to these models, there are also variants of each of these. Usually it amounts to a difference in the amount of storage. There are also various bundles that pack in games or peripherals like Kinect.

It seems clear that for almost any way you could judge the three, the Xbox 360 S is the winner. The only advantages the E has is similarity in design to the Xbox One, and perhaps a slight noise difference. The "classic" 360 is probably cheaper, but buying one used is slightly risky.

There's some more detail and a somewhat-useful table in this Wikipedia article.