I think it would be fair to define a "skylight" as a window in the roof that you can see the sky and clouds through. Some of them now use frosted glazings, so you can't quite see through them, but they are still basically designed like a window with a deep skylight well below them.
A "light well" is natural light that shows up someplace inside your house, almost like magic. You don't see outside, but the shifting natural light from outdoors shines into dark areas of your house, like stairwells, and even basement rooms. This is done by installing a relatively small, round skylight-like bubble on the roof. And below it, rather than a traditional skylight well, you install a large tube that has a mirror-like interior surface. This bounces the light down, around curves and obstructions, and as far down into the house as you want to go. Finally, it shines the light onto a small glazed dome on a ceiling somewhere inside your house. The dome looks very much like a modern light fixture, only it varies with the natural outdoor light.
Properly installed (leakproof on the ceiling and absolutely air tight all along the duct as well as at the ceiling), it has no condensation or cleaning problems. You can't see the birds fly by, but it is energy efficient, doesn't overheat the house in the summer, and gives you that sense of the outdoors deep inside your dark house.
The light well that we installed on the TV show was from a company called Solatube. The Toronto tradespeople who helped with this installation: Den's Quality Roofing, and Accurate Electrical (Keith, a really great guy).