Step 1: Understand the unit cell dimensions.
In the tetragonal crystal system, two of the axes have equal lengths, and the angles between all axes are 90°.
Step 2: Conclusion.
Thus, the correct unit cell dimensions are \( a = b \neq c \), and the angles \( \alpha = \beta = 90^\circ \).
Final Answer:
\[
\boxed{C}
\]