Right.
I'm always learning something new in this craft, and I've expanded my interpretation of square rule since I wrote that "Introduction to layout" article to include snap line square rule. As long as we are getting good results and understand the methods to get there, the definitions, while confusing now, can best be clarified by discussions such as this.
The distinction for me (and maybe only me) remains either bringing the joinery shoulders to match an irregular surface (scribing) or bringing it into a housing that is referenced off a snap line, centered or otherwise (square rule). Can you provide an example of how the traditional eastern methods are different from either of those? This might be worthy of an article in Timber Framing.