First, forget about CIE Lab color unless you already have a background in color theory. It's there. Photoshop uses it in the background, but you needn't concern yourself with it. The other three models—HSB, RGB, and CMYK—will have much greater impact on your work in Photoshop. The difference between the modes and the models is simple. The models are methods of defining color. Modes are methods of working with color based on the models. HSB is the only model without a directly corresponding mode. CMYK and RGB have corresponding modes in Photoshop. There are also modes for black-and-white, grayscale, and limited color work.
The Photoshop modes available under Image→Mode are as follows: