In this case, they're the same mechanism. The physics community has avoided the issue of "how are the laws of physics implemented"; they have dodged and avoided any kind of aether medium because mediums don't satisfy the postulates of SR. So I found a medium that did. I used the whole E&M spectrum, removed all the energy, and made the medium out of that. What remains are aether medium waves. They are the infrastructure that give the vacuum of space its properties. They are aetherial and easily overlooked. Aether waves transmit energy as E&M waves and photons; they even store energy as massive particles. But they are too subtle too detect. The wave-function (which is a math solution for quantum mechanics problems) is the closest that science can come to understanding these waves.Equivalent doesn't mean "the same mechanism" in general.
The result is that now everything is made of these waves, even gravity. Since gravity will frequency shift light, then acceleration fields in general occur when the whole EM frequency band is frequency shifted.
Yes, gravity is caused by large amounts of mass and energy, so large that the "fabric of space-time" starts to curve. These aether waves are the "fabric of space-time". GR describes the behavior of these aether waves.Gravitational and inertial acceleration are equivalent, but in the first case acceleration is due to a gravitating mass, in the second case can be a lot of things including gravity.But emitting radiation at different frequencies does not shift the frequency of the radiation. In free space each photon will have the same frequency it had when it was emitted. You're saying a frequency spectrum (a mixture of different frequencies) is a frequency shift. It isn't.
Any massive particle is an inertial reference frame unto itself. The particle is a kink in the aether waves; the mass of the particle is a particular configuration of the aether waves such that energy is stored in the particle.
A photon is thought to be independent of everything, including a medium. But if that were the case, then the photon would have no reason to obey conservation of energy nor would it have any reason to interact with anything. Instead, the photon is an excitation of the waves of the aether medium. The waves are interconnected with everything, all matter, all energy. That allows the photon(s) to conserve energy.To change a frequency you need to do something else than emit another frequency, because all you have then is two frequencies. It doesn't matter if the two are emitted at different times or the same time. This is especially true of EM radiation because photons have no effect on each other.
When a photon falls into the gravity well of a black hole, the well itself is a configuration of the aether waves. Specifically, the entire EM band blueshifts up to the event horizon. Photons that fall into or escape from the gravity well are just excitations of these aether waves.
If you synthesize a train of 64 photons of increasing frequency, and you take care to line up their phases, then eventually, it becomes indistinguishable from a frequency shifted aether wave that is implementing an acceleration field.