Violet is spectral: it's a frequency at the short end of the spectrum, and a shorter frequency than our blue cone cells are tuned to detect. So really it should appear dark blue, but in fact when we look at it the red cones, which are activated by long wavelengths, send some amount of signal too. This is due to a bug.

Purple, meanwhile, is a genuine mixture of short and long wavelengths, causing the same response.