I don't think there is any semantic difference, Yuriya. That being said, I hear "turned red/black etc." most frequently. I occasionally hear "turn to red" used by people who are talking about the change in color of leaves in the fall. I'm not sure that I've ever heard or read "turn into red" although it's certainly possible that I have. It does sound unusual, though.
In your first example "turn" can be interpreted as "become", for instance you would say:
His face turned red. meaning His face became red.
But I think in your second example, the verb "turn" is synonymous with "change", so you could say that a particular color turns from yellow to red, as well as you could say it changes from yellow to red.