There’s a difference between full-spectrum and daylight artificial lighting, and there’s even a lack of agreement about the terminology.
Natural sunlight contains a mix of all the varying wavelengths from the entire spectrum of visible light. It’s the mix of all these wavelengths that creates real daylight. Most so-called daylight lamps emit a much more restricted range of wavelengths that imitate real daylight by emitting wavelengths that concentrate on the average of those that natural sunlight contains. It looks about right to our eyes, but use a film camera to take a photo or try to grow plants in those conditions and things won’t go as planned. For the same reason, one’s perception of color can’t really be completely trusted in that kind of lighting.
Full-spectrum lighting, on the other hand, is an attempt at producing light with all the wavelengths present in just the right mix to simulate natural daylight. This is much harder to do since it requires a light source (or combinations of light sources) capable of emitting light in all the right frequencies and in just the right proportions to each other.
In other words, artificial light in the 5,000 to 6,000 kelvin range of sunlight isn’t necessarily equivalent to natural light. In addition, there’s another measurement to consider which is called the Color Rendering Index (CRI). Natural sunlight has a CRI of 100. CRI is a measurement of how accurately light reflects off objects in the colors that would be seen in natural sunlight. Some full-spectrum lights claim a CRI up to around 99. In addition, there’s a Correlated Color Temperature specification, but that’s another tangent.