Yes, this is essentially correct.
To go into a little more detail, here is what's happening on each of the three types of video inputs:
Composite: The signal is a combination of three signals that are referred to as Y, U and V. Y is the luminance, also called luma. U and V carry the color information, called chroma, which are mixed with a carrier signal. The consequence of all this mixing is that you get interference between the signals which results in things like "dot crawl," color bleeding, and other issues.
S-Video: S-Video is basically like having two composite signals in one. If you look at an S-video cable you see four pins. One of those pins carries the Y, and the other carries the U and the V (they each have their own ground). This greatly cuts down on the amount of interference and visual artifacts you get from composite.
Component: Component, also called YPbPr, takes things a step further again. The Y cable carries Y by itself (luma); the other two cables carry the differences between blue or red and the luma signal, respectively. Green is not necessary to be carried because you already have the blue, red and luma so you can mathematically determine what green is, and it saves bandwidth. Since each "component" of the signal is carried independently, YPbPr has the best video quality of the three.
There's actually a good visualization of the process at
http://en.wikipedia.org/wiki/YCbCr -- I recommend looking it up if you're curious.
As an aside -- the absolute ideal would be pure RGB, where you carry Red, Green, Blue, and then Horizontal and Vertical sync. It's completely "uncompressed," if you will, and that's why it renders the best possible picture, including all sorts of variations on Vsync and Hsync. But Component is pretty good as long as you stick to NTSC signals (525 lines, 60 fps interlaced, etc.).