Well said, all. Yet I can't resist!
IMHO: Square Rule is the means by which we layout and cut a "perfect" (dimensionally accurate and square) timber frame from "imperfect timbers". Reductions and dimensioning from a reference edge are tools that compensate for dimensional variations in timbers (i.e. an 8x8 that's 7-7/8 X 8-3/16 gets reduced to 7-1/2 X 7-1/2 AT THE JOINT.) This ensures that your reference edge-to- reference edge dimensions are correct. When a timber is straight and square, laying out from an edge will be sufficient to achieve this ("edge" rule or "mill" rule, I think of this as sort of a subset of square rule).
If the edges or faces are not straight and/or square we need to establish straight and square planes to use as references. This is when we snap lines on the stick to define these planes. I've heard this called "snap line square rule" or "true square rule" or just "square rule" as opposed to "edge" or "mill" rule.
I think most of us are on the same page but we have the usual vernacular differences. He calls it a wind brace, she calls it a knee brace. (***Not intended to start a discussion on different kinds of braces!***)
There you have it. Fee: $0.02 (waived)