There are several orthogonal issues here:
- The physical size of the film the movie was shot on (the negative).
- The physical size of the film the movie is projected from (the print).
- How the frame is composed on that film, which is related to the aspect ratio.
Some of the comments and other answers are conflating various aspects, which can cause more confusion than clarification. For example, others have implied the 70mm and IMAX are the same thing. While it's true IMAX does project from 70mm prints, 70mm prints are used in a variety of other, non-IMAX formats.
Before the switch to digital, most commercial movies were shot on 35mm negatives and then distributed to theaters as 35mm or sometimes 70mm prints. (Yes, some 70mm prints are sometimes made from 35mm masters.)
A few big budget, "big screen" movies were sometimes shot in 70mm and distributed to big theaters on 70mm prints and smaller theaters on 35mm prints.
The sizes, 35mm and 70mm, refer to the width of the film itself. This width includes the room for the sprocket holes and analogue audio tracks. Some digital audio tracks use the spaces between the sprocket holes. I believe (but correct me if I'm wrong) that magnetic audio tracks are not included in that width.
Most film runs through the projector vertically (big exceptions are true IMAX and VistaVision), so the width the frame is limited by the width of the film minus the width of the sprocket holes and analogue audio tracks. Thus the width of a frame on a 35mm print is a bit narrower than 35mm.
The sprocket holes are often called "perfs," and many formats are thus referred to as a number of "perfs." That is, as the number of sprocket holes from one frame to the next. A typical frame size for 35mm prints is 4-perf. Thus the height of the frame was limited by that number. For 70mm, I believe common formats were 7-perf, but I don't have a source for that.
The aspect ratio is the ratio of the width to the height. In olden times, movies were pretty square, much like old television sets. To compete with television, the studios introduced different aspect ratios (typically wider) in order to make the movie experience seem more immersive than television.
Given that the width and height of the frame both have upper bounds, there are only a few ways to adjust the aspect ratio:
Use less than the full height available on the frame, and use a telephoto projection lens to compensate for the diminished height.
Shoot (or print) the frames with an anamorphic lens that squishes the image horizontally to fit it onto the film, then project with the complementary lens that stretches it back out. This is typically done for the widest of wide-screen formats. A telltale artifact is that lens flares appear as ovals rather than circles.
Run the film horizontally. The height is limited by the film size minus sprocket holes, and the width is limited by however many perfs you choose. This is what traditional IMAX does. (Traditional IMAX also uses 70mm film exclusively.)
Given identical aspect ratios, 70mm film gives far more area per frame, which means it can be projected larger or will have better clarity and detail when projected as the same size as a comparable 35mm print.
Some movies are shot in a variety of formats, but mastered into a common format during editing and post production. For example, the original Star Wars films used old VistaVision cameras for many of the motion-controlled model shots, even though everything else was probably shot with traditional cameras that ran the film vertically.
In the case of this Tarantino film, I suspect it was shot on 70mm using anamorphic lenses in order to make a super-widescreen. IMDB confirms.