When Process K-14 was introduced in early 1974, there were two films, K-25 and K-64. There was one version of the process. The machines for 35mm film ran about 50 to 80 feet per minute. The K-40 super 8 movie film came a year later. The super 8 film was processed in machines that ran about 250 feet per minute. The increased transport speed resulted in increased agitation and increased development. The solutions were all the same, but the agitation was different. It was different enough that when they started to work on the type A slide film, they found they couldn't use the same film for super 8 and 35mm. They had to build a separate K-40 type A film for 35mm slides. The 16mm movie film and the regular 8 movie film (which is 16mm wide until after it is processed) were the same emulsion as the 35mm slide film. At this point we have several different films and two versions of the process, one for super 8 and one for 16mm and 35mm.
That's pretty straight forward so far, right?
When the 120 format was introduced, it was necessary to increase the agitation significantly to get decent uniformity. Since the agitation increases development, the developer formulations were adjusted to compensate. Rather than run separate developers in 135 and 120 machines, the agitation was increased in the 135 machines as well. By 1990, most Kodachrome was processed in high agitation processors. There was a difference in the developers between the wide formats and the super 8 machines. (The super 8 machines were still using the original formulas.) Now we have two sets of formulas, but nearly everything is high agitation.
There have always been some labs that only had 35mm machines that would process super 8. The results were a bit off in contrast and color balance.
In the early 90's, K-Lab was introduced to make K-14 processing more available. These machines were smaller than others, but they maintained the high agitation option.
Is everything clear? Probably clear as mud. Anyway, we don't have to worry about machine-to-machine differences any more.