Cinemascope, the first widely adopted widescreen process, had an aspect ratio of 2.35:1. It was an anamorphic process that used a special lens to squeeze the image onto a standard 1.33:1 film negative. A special lens on the projector unsqueezed the image onto the 2.35:1 screen in the cinema.
Cinemascope lenses were expensive, slow, induced distortion in early years, and had shallow depth of field. Looking for a cheaper alternative, the studios settled on a compromised ratio using standard lenses. Films were shot full frame, 1.33:1, but lines in the viewfinder outlined the widescreen viewing area, within which the director and his DP would compose the action. Although action outside the viewing area would be recorded on the negative, it was not meant to be seen later; it was merely a byproduct of the process. When the films were projected, a "soft" matte in the projector masked the exposed footage on the print outside the widescreen area; the area within was blown up to fit the wider screen in the theater. The one drawback to this process was that since a smaller area of the frame was being blown up to fill the big screen, more grain would be apparent in the projected image.
Aspect ratios for these non-anamorphic widescreen movies varied in the early years, ranging from 1.66:1 to 1.75:1 to 1.85:1, finally settling on the latter in the mid to late fifties, when TOE was shot.
1.66:1 and 1.75:1 remained popular formats in Europe during this period, which explains why The Trial and Chimes at Midnight would have been composed and projected at 1.66:1.
In some instances, films were shot with a "hard" matte, meaning that the matte was in the camera, and the area on the negative outside the widescreen outline would not be exposed, and print black, but this was rare. Because aspect ratios varied in theaters, depending on where the film was shown, a certain flexibility was needed. The "soft" matte solved that.
So, TOE was shot both full-frame and 1.85:1, because, during the shooting process, that amounts to the same thing, but it was composed for 1.85:1, and meant to be projected that way, at least in the big first run U.S. theaters. I doubt that concern for future television showings was a major factor in 1958; certainly when 2.35:1 anamorphic movies were shown on tube no one cared that half the image was chopped off. The point was to fill the whole screen on those little early TV's. When movies like TOE were shown, this was easy to accomplish, they were projected without the "soft" mattes and that was that. It is only later, with directors like James Cameron and processes like Super 35 that movies were composed with both media in mind. Yeah, you got more of the image rather than less, but that doesn't mean that the full-frame version of a 1.85:1 film is the correct one. It isn't.
Sorry guys, Schmidlin is right on this. But that being said, although 1.85:1 is the "official" ratio, TOE was most likely shown in Europe at 1.66:1 or 1.75:1 (which explains Sergio's observation that the print of TOE used for the London revival indicated 1.66:1), and even full frame in some venues there and in the U.S.. Unfortunately, one has to make choices, and 1.85:1 is probably the best one.