From what I recall, full spectrum is used to imply something similar to "daylight" which represents (or simulates) the colour temperature, the balance/ratios of the amount of output at each point of the spectrum and colour rendering of noon sunlight.

Great for stuff like shopping, including clothing and food, but not the most attractive for the home because of its stark/moodless appearance. They're also good for certain types of animal habitats, including specialty products with decent UVB output.

If you look at a graph of the output spectrum of various lamps you'll see dramatic differences, including the miniscule amount of output at certain wavelengths that would "logically" disqualify a particular lamp from being called "full spectrum."