There are different units for the same thing (Fahrenheit and Celsius temperature scales), and there are similar units for slightly different things (troy ounces and avoirdupois ounces). Measuring light is no different, because there have been many methods of measuring it proposed over the years and different groups will use differing units or methods. I'll try to give you a basic understanding of the differences for the common measurements of light, how they are used, and what they actually mean.
Candle-power or CandelaOne candle-power is the amount of light put out by a single standard candle. The “standard” candle was a pure whale wax (Spermaceti) candle weighing 1/6th of a pound, burning at a rate of 120 grains (there are 7000 grains in a pound) per hour. Any normal candle will put out about the same amount of light, so don't worry about the details too much.
The total output of light in the visible part of the spectrum. Used for measuring the total amount of light produced by a source, most often used when comparing flood- or lantern-type lights. Household light bulbs will have their output listed in Lumens since they radiate light in a spherical manner. The light produced is what is measured in Lumens, but the light falling on a surface is measured in Lux or Foot-candles.
The metric unit of measure for illumination of a surface. Most commonly used when comparing spot-type light sources. One lux is equal to one lumen per square meter. A good example is a flashlight with a variable focus, like a Mag-Lite. The bulb puts out a steady amount of light (Lumens) but by changing the focus you can concentrate that light into a smaller area, making it brighter (Lux).
A foot-candle is actually one lumen of light density per square foot of a target one foot from the source of light, and is the American (SI) version of the Lux. Since most of what is sold in the US is made in countries that use the metric system, it's not likely that you'll see foot-candles listed on new lights.
WattSome lights are advertised by the wattage of their LED or bulb. Watts do not relate directly to the light output level. As used for light sources, Watts defines the rate of energy consumption by an electrical device when it is in operation. Differences in the efficiency of the LED or bulb as well as in the amount of light produced that is visible to the human eye make it difficult to relate Watts of power usage to light output.
I hope that clears up some of the confusion about the different units. I managed to keep most of that pesky math out of it while I did it, too.