These are some extremely detailed definitions and I don't even have the math to say if they are correct. But what does it all mean to the user?
If you draw -- say, a fish -- in Photoshop, you will essentially be spraying loose pixels into a window. You can do some neat things with that, but if you scale, rotate, or distort your fish, your results may not be good. The curve -- say, the belly -- may start to look jaggy; it may start to look as if it were built out of little blocks. And if you drew a yellow fish against blue water, Photoshop will make this look good by anti-aliasing -- by drawing some of the pixels along the curve in various shades of green. If you change your mind, and decide the water will be, say, pink, the curve will look all wrong. This is because Photoshop does not know that the belly is a curve, or anything else. Once drawn, the fish and the water are all equally loose pixels.
If you draw the same fish in Freehand, using bezier curves -- with the pen tool -- Freehand remembers those curves as curves. Whenever the program attempts to render, or draw the curve onscreen or on paper, it will convert it to pixels. It will do this conversion freshly for each and every new render. You can transform the curve -- rotate it, even change its shape -- and it will not fall apart into a jaggy scratch.
In Freehand, a bezier curve appears as the curve itself, together with its control points. Drag the control points to change the shape of the curve. A little hands-on experimentation will make it clear what's happenning, and no math is needed.
Other shapes, such as circles, are internally drawn with bezier curves. If you draw a small circle in Photoshop, and scale it up, it will look like a blob. But if you draw even a tiny circle in Freehand, and scale it way up to look very big, it will still be a perfect circle. If you select the circle and choose "Ungroup" and "Unjoin", it will come apart into the bezier curves of which it is made, and you can alter them as you would any other.
A good way to make complex drawings is to make all the basic shapes in Freehand, then export them as one or more EPS files. You can import EPS into Photoshop, which will do a high-quality render; at this time, you can composite, and apply shading and special effects. If you later need a larger rendering, or need to change the background or rotation; go back to the EPS file, import it again, and work with the new rendering.