But even full-spectrum light can be different depending on the source, that’s why we have a white-balance control. And even with full-spectrum sources you can get mixed lighting. Have a look at a sunny snow-landscape: either the shades are blueish (“cold”), or the sunny areas are orangy (“warm”).
Unless, of course, someone has been messing around with masks.
So “standard illumination” has a colour temperature prescribed (temperature in K of a black body that radiates the light you want), which fully specifies the spectral composition.