Very basic guide (and I make no claim to be an expert). Please correct me or add more to it everyone. A lot more detail could potentially be added.
Incandescent:
The normal type of lamp used in homes with a standard bayonnet or screw-in fitting. Normally found in smaller, older aquariums. Disadvantage - they get very hot and are not very efficient.
Fluorescent:
By far the most popular and useful. Efficient but larger wattages get quite long and will therefore not fit over smaller tanks. Usually multiple tubes are used to increase light. Require a ballast and starter (see below) which connect to fittings on both ends of the tube. The colour output/spectrum is specified in kelvin (k). The diameter of the tube is specified in eights-of-an-inch preceeded with a 'T', i.e. T8=1 inch, T5=5-eights-of-an-inch, etc.
Fluorescent controller/ballast/starter/convertagear:
The electronics that drives a fluorescent tube. Contain a ballast (the electronics) and a starter (choke) built in - normally referred to as just 'ballast' or 'starter'. Similar ones are used to drive power compacts (see below) and these are normally referred to as 'controllers'.
Compact fluorescent / Power compact (T5):
Relatively new, becoming more and more popular. Compared to standard fluorescent they are more efficient, larger output lamps are available in much smaller sizes and they do not give off as much heat. This makes them suitable for use over smaller aquariums. They are relatively expensive however. Require a controller to drive them (see above) which connects to a 4-pin connector at only one end of the lamp. A square connector is known as Japanese or Panasonic and a straight connector (4 pins in a row) are known as European.
Energy saving power compact incandescent fitting:
These are power compact fluorescents designed to replace standard incandescent lamps. Normally just called 'energy saving lamp/bulb'. They have the controller (see above) built in, so they can fit straight in to an incandescent light socket. Very suitable for use over a small aquarium and an ideal choice for those aquariums with an incadescent fitting.
Metal Halide:
Large, very expensive, not very efficient and get extremely hot. These are normally used by hydroponics people and serious marine setups because of their ability to penetrate deep. Often suspended from the ceiling above the aquarium and not built into hoods because of size and heat.
Other information:
here is a thread I found with more indepth info.
How fluorescent lamps work
How fluorescent starters work
Are fluorescent bulbs really more efficient than normal light bulbs?
(all pictures are taken from google-images.)
