The two devices do entirely different things.

Extension tube:

• An empty tube which moves the lens further away from the sensor.
• The point is that as you focus on closer and closer objects, the focused image (which you want to place on the sensor) moves further from the lens. Eventually the lens reaches the limit of its travel and closer objects focus behind the sensor. Adding an extension tube gives you more room to do this, so you can focus on closer objects.

Teleconverter:

• Contains optical elements which increase the focal length of your lens.
• As a consequence, the maximum aperture shrinks (making the lens slower).
• For example, a 300mm f/2.8 with a 1.4x TC becomes a 420mm f/4 (you lose one stop), and with a 2x TC it becomes a 600mm f/5.6 (you lose two stops).
• Typically, TCs work best with telephoto lenses.
• Teleconverters can make autofocus stop working by reducing the maximum aperture beyond the limit of the autofocus system (often f/5.6). For example, adding a 2x TC to a f/4 lens results in a f/8 lens, which probably won't autofocus.
• Also, adding elements to a lens degrades its quality somewhat; this may or may not be a visible problem. Generally, you will want a lens and TC which are designed to work together to minimize this issue.

Both (if good-quality) contain mechanics and electronics to let the lens and body "talk", to keep auto-focus and metering working.