Human blood is always red, even blood in the body that is oxygen-deprived and heading back toward the lungs to refuel.
Veins close to the skin show through as purply blue or greyish blue because that’s their color.
The term blue blood as it’s used regarding royalty comes from the fact that royalty didn’t get outside much. Peasants and regular workers were browned by the sun, so their blue veins were less likely to show.
The white skin of European nobles showed off their blue veins, and people assumed their blood was blue as well.