[uvfyxxbe] Color and temperature radiation

Why is it that the rainbow goes red orange yellow GREEN blue violet, but color of black body radiators (e.g., stars) as temperature increases goes red orange yellow WHITE blue violet?

Almost the same except GREEN versus WHITE.

I think I mostly know the answer in that each band of the rainbow is a narrow spectrum, but the black body radiator emits a broad spectrum which interacts with the color receptors in our eye perceiving white, even though the peak is at green.