I think it's always important to completely understand and keep in mind what's might be meant by a "routing" and what may not be.
Essentially a complete routing can be a particular sequence of distance and direction related "pieces" (holes). Sometimes called a "stick routing" (which certainly can be a complete routing) it can be nothing more than a dot (tee) with a line connecting another dot (green site) and on and on in a series of connected pieces.
In my mind it's certainly possible for two architect to use the exact same "stick routing" and come up with two golf courses that can be quite different. The reason for that, in my opinion, is the vast difference in actually "designing" an exactly similar "stick routing" can just make it so. Green sizes, shapes, orientation, bunker schemes, fairway sizes and lines, not to mention various earth-moving schemes on the same landform can simply make two identical routings into two courses that may almost be unrecognizable from the other.
A routing has been called the "bones" of a golf course and I think that's so. Probably more appropriately a routing should be called the "skeletion" of a golf course.
But we know that all human beings basically have fairly similar skeletal structures but are the similar people, similar looking, similar acting etc? Of course not.
The same is true for a routing as opposed to the "designing" of that routing---the "designing up" phase can make identical routings appear to be almost completely separate courses, in my opinion.
Such is the nature of the eternal "jigsaw puzzle" of golf course architecture!