No, it's actually the red sun what gave him powers. He is a superman thanks to that origin. Maybe other suns other colors would also change him, but we're talking about Earth.
Of course, the thing about stars is that they all emit the same kind of energies: red sun radiation = yellow sun radiation = white sun radiation, etc, etc. The differences in color have to do with differences in temperature, nothing more.
But, hey, comics...
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Shinier than a speeding bullet.
Under the light of a red sun, he is powerless and mortal, as are all Kryptonians. Under the light of a yellow sun, Krytonians are practically omnipotent.
The reason why kryptonite is so deadly to him is because it has RED sun radiation on it, from when Kryptons' red sun exploded. The red radiation slowly drains his powers, and since the red radiation is sapping his powers, it is causing intense pain because its red radiation, which makes Kryptonians mortal.