We can make LED light appear to be any given colour by mixing multiple LEDs. But mixed colour isn't the same as pure colour, made from a single spectra of light. Nor is it the same as true broad spectrum light - like we get from black-body radiation like the sun, or a tungsten bulb.
Its hard to tell the difference just by looking at a light. But different kinds of lights - even lights which look the same colour - will change what objects actually look like. And they probably have different effects on our sleep cycle and our low light vision. I was in a room once lit only by sodium vapour lights. The lights were yellow, but everything in the room (including me) appeared to be in greyscale. It was uncanny.
This is part of the reason why LED lights are still looked down on by a lot of old school photographers and film makers. Skin doesn't look as good under cheap LED lights.