I'm aware of two devices that can extend the reach of a lens: the teleconverter and the extension tubes. What else would they have in common, and where do they differ?
Are there situations where one would be preferable over the other?
The two devices do entirely different things.
Both (if good-quality) contain mechanics and electronics to let the lens and body "talk", to keep auto-focus and metering working.
An extension tube has no optical components. It's role is to move the lens further away from film/sensor. This results in a "closer" focus, which makes it more ideal for macro photography. The downside is that with some extension tubes you lose AF, and with all tubes, you require more light for the exposure, as light falloff becomes an issue.
A teleconverter, increase the focal length of a lens. Common TC are 1.4x and 2.0 multipliers. The TC has optical elements which increases the zoom range of certain lenses (not all lenses will work with a TC). The downside is a reducing in the maximum aperture of the lens and some degradation in overall image quality. TC's are a low-cost way to go "long" with your telephoto lenses. When you need the extra reach of a super telephoto lens, pairing a TC with an existing telephoto lens is a very economical solution, at the expense of optical quality, a darker view finder, and potentially manual focus only scenario (most bodies lose AF abilities unless the lens has a certain max aperture)
A teleconverter and an extension tube are pretty much each others opposite.
A teleconverter is used to increase the focal length, for example turning a 70-200 zoom into a 140-400 zoom. It has lenses to preserve the characteristics of the lens.
An extension tube is used for macro photo, turning a standard lens into a macro lens by reducing the closest focusing distance (and reducing the longest focusing distance also).
So, if you want to take images at a long distance, you can use a teleconverter, and if you want to take extreme close-ups, you can use an extension tube.
(You could even use both, but they don't cancel each other out, you still end up with a macro lens.)