Two Different Qubit States

There are two different qubit states for each pair of measurement probabilities of $|0\rangle$ and $|1\rangle$. For instance, the states $\frac{\alpha|0\rangle+\beta|1\rangle}{2}$ and $\frac{\alpha|0\rangle-\beta|1\rangle}{2}$ have the identical measurement probabilities, as does any pair of states, such as $|\psi\rangle$ and $|\psi'\rangle$ whose state vector is mirrored at the Z-axis. This is depicted in the following image.