"Full Spectrum" is a term that gets tossed around lightly among light bulb manufacturers, but the true and correct meaning is a source of light that has a Color Rendering Index of 100.
Color Rendering Index, or CRI, is a measure from 1-100 of how well a source of light reproduces colors. If you've ever tried to view something colorful using a cheap LED or a parking lot sodium halide light, you'll note that the number of colors and color differences you see are reduced - everything is just sublimated down to a few unique colors. These would be low-CRI sources. A good halogen bulb or sunlight reproduces colors best, thus earning a 100 CRI score, or true Full Spectrum lighting.
Another thing to take into consideration is Color Temperature, or "tint". This is measured in Kelvin, usually from low 2000's to 10k and beyond. The lower this number, the "warmer" or more yellow/orange the color source, and the higher, the bluer. There is no standard for "true white" or "perfect white", though it's generally considered to be somewhere around 4000 Kelvin. Keep in mind that a light source can have a profoundly warm or cold tint and still have a 100 CRI score - a good example being ambient light around sunrise or sunset; this light is quite warm and tints everything orange, but is still 100 CRI because all colors are rendered, they're just shifted notably towards orange.
All this adds an extra layer of difficulty to finding a good "Full Spectrum" light, because even with a 100 CRI, the colors will still not look correct due to the tint. Household halogen light bulbs have this problem, they are indeed full spectrum, but they're slightly warm, so everything looks a bit yellow.
I've been searching for the perfect bulb for some time, and the closest I've come thus far are CFL bulbs from Sylvania - their 3500K bulb isn't true full spectrum, but it does have a remarkably neutral white tint, and reproduces colors better than most incandescents I've seen. The 3000K bulb is the same thing with a warmer tint, better for general household use (3500K is better for bathroom/office/craft-art room, etc). Definitely worth a try if you run across one, they're usually sold at Lowe's.