I have recently referred to the "v3.40 branch" of MS-DOS. This refers to the v4.00 and v4.01 versions that are well known and that have shipped most sources in the 2024 April release.

The v3.40 distinction is as opposed to the "European MS-DOS v4.00", "Multitasking MS-DOS", or the "v4.00 Ozzie" version. This one unfortunately lacks most of its sources.

Now, where does "v3.40" come from? There are two sources of this term:

This is a variable in the DOS Swappable Data Area called the DOS34_FLAG. The comment calls it "common flag for DOS 3.4". (The values for this word are given in the file devsym.mac.)

In the Interrupt List's list of the MS-DOS v4 SDA, it is called "DOS 3.4 (European MS-DOS 4.00) bit flags". For one, this indicates that the "DOS 3.4 flags" term leaked in some way to be incorporated into the Interrupt List before the release of the sources.

For another, I think it's mistaken about the "European MS-DOS v4.00" bit. I think MS-DOS v3.40 was a term for the regular (non-multitasking) MS-DOS branch that was eventually released as v4.00. This is specifically in opposition to the "European" branch.

The version fake table, or special entries list, is the MS-DOS v4.00 incarnation of what later became SETVER. Interestingly, the faked version number in the default list is always the 3.40 version. So it stands to reason that v3.40 was considered the successor of v3.20, v3.30, or v3.31.

I believe that v3.40 may have been the name for the branch that became the non-multitasking v4.00 while the multitasking v4.00 probably started out as the original "v4", the idea being that it was a crass departure from the v3 branch while v3.40 was a continuation with fewer differences (such as the support for 32-bit sector numbers, hash buckets for buffers, and the Extended Open/Create system call).