“White” or “6500k” do not tell the whole story.
This is the spectrum of a 6500k LED, it has a pretty “full spectrum” in the visible wavelengths
This is the spectrum of a 6500k Giesemann Tropic T5 bulb. Much less smooth, but includes more light north of 700 nm and should have some UV leakage at around 365 nm.
This is the spectrum of a 6500k Iwasaki MH bulb.
Very “full spectrum” from UV all the way to IR, and is the closest of the three to sunlight.
This is the spectrum of typical 6500k daylight:
This spectrum changes of course the deeper into the ocean you go.