All the three stepper motors might or might not be the same. This exclusively depends on the model of the printer. However, one can definitely use same motors for all the three axis.
Regarding the second part of the question, as to how to choose the stepper motors for replacements, there are several factors one needs to consider. First factor is the form factor. You need to search for a motor which would fit into the existing slot or assigned place. If it is different you would have to do a lot of tweaking.
Secondly, you need to consider the torque of the motor. You need to verify the amount of current that is required for the motor to achieve the necessary torque. Will the board support such an amount of current?
Finding out answers for these questions on form factor, torque and driving current will ease the process of sourcing the correct replacements.