<"I believe the definition of each type is determined by wavelength. The energy is determined by both wavelenth and amplitude."

The "amplitude" in this case is the number of photons and so two 60keV
X-rays have 120keV energy. In any reference frame, a photon has a discrete energy(proportional to frequency, inversely to wavelength), polarization and direction of propagation.

A short wavelength high intensity x-ray can have more energy than a low intensity long wavlength gamma-ray.

Sorry Mark. Gamma rays by definition are the region of the EM spectrum with shorter wavelength (higher photon energy and frequency) than X-rays. A photon of 100keV you could call an X-ray or Gamma Ray but it doesn't change the fundamental properties.