I understand it this way (through conversations with 3 different US engineers who started their careers between 1926 and 1945):
In the early part of the 1900's engineers were a dominant group who prepared many of their plans by themselves. Engineering curricula required a development of drafting skills and individuals who simply were "draftsman" or "draughtsman" were not very prevalent.
Generally, young graduate engineers would come into employment with established engineers (usually an engineer who was a sole proprietor or a partnership of some kind). These young engineers would simply draw for the primary engineer for a long period of time before the chief engineer would trust the younger ones to do design work. I think conditions are similar today, but with a shorter learning curve as projects seem to come and go at a much faster pace.
These older gentlemen that I worked under in the 1980's all came through this process. They were very good at ink on linen drafting and were very meticulous in their designs.
I think that sometime in more recent years (perhaps the 1950's after WW II) the use of non-engineer educated draftsman came into use as the post-war years saw a boom in construction and the need for quicker turn-around in projects compelled the engineers to limit their drawing and focus on design.
The increased complexity of the building codes, higher specialization of engineering disciplines, and an increased awareness of productivity needs in the engineering industry also added to the use of non-engineer drafstman.
So there wasn't necessarily a SEPARATION, but an addition of technical personnel to the engineering office.
Today, we have AutoCADD, etc. that requires another complete level of specialization, although CADD software does seem to be getting easier to use. Many engineering firms do not use "techs" anymore but compel their engineers to do all their drawing. I think this is the trend of the future as CAD becoms CADD (adding Design to the drafting software).
A complete synthesis of drawing and design is coming so the age of techs may be limited to that of a department guru keeping engineers productive on the software...who knows.
Anyway...that's my take on it. Interesting question.