> Since they have the same rotation angle per step, I shouldn't have to calibrate the new model, right? (I'll use the original wheel)
Yes, you do not have to change anything, other than the Vref of the stepper driver.
> Did the vendor send me a motor with inferior performances?
Yes, the one you received has a lower height, so smaller coils and smaller permanent magnets; basically lower torque.
> Will my performances degrade if I use the new motor?
That depends on the loading of the carriage of the X-axis, it could if it is heavy; you now have less torque available to move the carriage. But, this type is frequently found in 3D printer kits and should work.