Context is important. If a physicist is studying processes involving only gamma radiation specifically, he might refer to it as “gamma radiation.” Or he might just say “emits a photon”, or “light of wavelength X”, or any number of ways. It may depend on his individual style, the intended audience, the putting on or off of an informal or formal affect, and just, well, how it sounds in the context of the rest of the paper. Either way, as a physicist I can assure you that “light” is understood to mean “electromagnetic radiation.” That is why there is such terms as “visible light,” and “infrared light.” The word “light” requires a modifier if one wants specifically to to refer to the visible part of the electromagnetic spectrum. The reasons some other forms of light are referred to as “waves” or “rays” is because, in addition to being a type of light, they have other properties that are good for lending names. After all, it’s nice to have a name for something. Microwaves and radiowaves are very large “waves” of light, for example.
The reason is that “light” was the first part of the electromagnetic spectrum to come into popular usage. Next came the discovery of infrared light, and then ultraviolet light. They were thought of as “invisible” types of light that extended just beyond the rainbow you might see when you send light through a prism. So at the time both were referred to as types of “light” because of the ways in which they were discovered: as extensions to the rainbow of colors of visible light. Infrared (just before red) and ultra violet (just past violet). So already at the time of their discovery, different parts of the electromagnetic spectrum were understood to be part of the same underlying phenomena, and were referred to collectively as “light.” You say this is “history of the matter, not in the physical facts” but in this case it was precisely the physical facts that determined the history. Next came the discovery of Maxwell’s equations, which put all forms of electromagnetic radiation under one umbrella. It predicted things like radio and microwaves, which were looked for, and found. Historically these were, and still are, often referred to as “waves” because that is exactly what they are, macroscopic waves of light. For a similar reason, parts of the other end of the spectrum are often referred to as “rays.” So each type of radiation has a history associated with it and a unique name that it was given shortly after its discovery, but each were understood to be an extension of the spectrum initially referred to as “light.” Since “visible light” was not “discovered”, no new name was given to it. It had always been known as “light.” And its colloquial use remained, but in scientific circles the solution, at the time, was to start referring, in the case of ambiguity, to the visible spectrum as “visible light,” and extended electromagnetic spectrum simply as extended frequencies of “light.”
Historically, the popular terms come from the terms physicists use. I am explaining to you that physicists use the term “light” out of convenience. I’ve described some more of the history above, in case the OP is interested, although I disagree with you that that is what the OP is really asking. He references information and gravity, which are not any kind of “light” at all, and yet the speed c is obeyed by both. I think the OP is asking whether light is physically special or not. The answer is that it is not special. Light just happens to be massless, and in great quantity.
