White light from the sun, or daylight lamps, contain almost all colors of the spectrum.
White light from LEDs (might) only contain a fraction of the spectrum, just enough to look white.
The amount of spectrum a white light contains is related to the Color Rendering Index (CRI) of that light.
You can see an example of an incandescent lamp and a fluorescent one together with their spectrum on wikipedia: [https://en.wikipedia.org/wiki/Color_rendering_index](https://en.wikipedia.org/wiki/Color_rendering_index)
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