They're states but not eigenstates. It's like the difference between RGB colour and greyscale. In both cases there are infinitely many possible colours, but in greyscale they're all mixtures of two "primary" colours (black and white) whereas in RGB they're mixture of four (black, red, green and blue).
In a qubit the infinitely many superposition states are all mixtures of just two eigenstates.
In a qubit the infinitely many superposition states are all mixtures of just two eigenstates.