X-rays and γ-rays of same energies are distinguished by their:

The X-rays and the γ-rays of the same energy cannot be distinguished from one another by frequency method as the frequency of a wave is the property of its energy. They both will have the same frequency and energy.

Both rays are neutral and so they can't be distinguished by charges or ionising power.
But the two waves will always have different methods of production. So, they can be differentiated by their method of production.