While that may be how the box is labeled, here in the US it's called 35mm.
If you ask a store clerk for "135 film" you'll get a blank stare.
And I challenge you to find a "135" camera. There are/were plenty of 35mm cameras.
- Leigh
Semantics are wonderful

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I totally agree that "35mm" is the common, every day, "Kleenex" reference, although I might point out that nowadays if you ask most store clerks for "film", you will get the same blank stare.
The point I was trying to make is that the actual designation for the film, packaged in a way that it can actually go into our still cameras and be used by them, is "135".
There are lots of types of 35mm film that are unusable in our cameras, although some of them can be made usable by packaging them appropriately into 135 packaging.
The 35mm film for motion picture cameras is one type of 35mm film. It has its own type of sprocket holes. You would use it in something like an Arriflex camera - common I guess in the motion picture world, but certainly not every-day. Unless you modify it in some way - cut it into appropriate lengths and load it into appropriate cassettes - you cannot use it in most common still cameras.
The 35mm film for motion picture projectors is another type of 35mm film. It has another type of sprockets. It too requires modification for use in "35mm" still cameras.
A third type of 35mm film is used in 126 cameras. That film has a really different type of sprockets, as well as backing paper and a 126 type of cartridge. There is no practical way of modifying this 35mm film for use in "35mm" still cameras.
The most common type of 35mm film for most of us here is one that has an emulsion suitable for still photography, the same sprocket holes as the motion projection stock, and a cassette that is suitable for cameras that take 135 film.
The "135" describes the combination of film size, sprockets and cassette - not just the film itself.
Historically, there were other styles of cassettes and packaging for 35mm film that allowed it to be used in what we would now describe as "non-standard" cameras. From Wikipedia: "The designations 235 and 435 refer to 35 mm film in daylight-loading spools, that could be loaded into Leica or Contax style reusable cassettes without need of a darkroom. The 335 was a daylight loading spool for the 24 × 23 mm stereo format."
I only have Kodak boxes to refer to, but while all have reference on them to 135 film, all but one of my individual film boxes have no reference to 35mm film. That exception is a roll of 1987 Kodachrome where, in addition to all the "135" references, there is a "35mm" adjacent to the DX symbol. In contrast, the bulk film rolls have no reference on them to "135" - it is "35mm x 100 feet" on them.
I've browsed through some Kodak datasheets. The individual rolls are referred to as 135, while the bulk rolls are referred to as 35mm.
I have a fair number of camera manuals within reach. Some refer to film as 35mm, some refer to both 135 and 35mm, many just say film and 24mm x 36mm.
It is similar to the 120 vs. 620 comparison. The film is identical but other factors (in this case the spools differences) determine the suitability for use in a camera.
I point out all this detail because while we have a lot of historical reference and context, that isn't the case for people who are new to film. Someone new might assume that all "35mm" film is suitable for use in something like a Canon AE-1, and end up buying an old 400 foot roll of "35mm" motion picture projection stock off of eBay thinking that it is perfect for their needs.