A bit of history for you. First nuclear radiation was discovered. At that time, though, it was not considered nuclear, because the concept of the atomic nucleus did not exist. Even the concepts of atoms and molecules were considered speculative. X rays were known, though, so initially it was thought it was the same thing. But then it was discovered that when this new radiation passed through electric or magnetic field, it would separate into three beams, which were called alpha, beta and gamma. Alpha and beta would bend in opposite directions, and gamma rays would continue straight on. Gamma rays seemed a lot like X rays, but were much more powerful.
So as you can see, "nuclear radiation" is more than just gamma radiation.
On the other hand, there is no real distinction between gamma and X-ray radiation. It is really the same thing. Historically, there was some distinction based on the wavelength because early X-ray generators were not very powerful, but this is no longer the case.