Perhaps if has to do with the fact that there are two equivalent ways to calculate the stdev.
The familiar way is find the differences, square them, and then sum the results:
s = [ sum( x(i) - x-bar)^2 / n-1 ] ^ (1/2)
It turns out you can also square first and then sum
s = [ sum( x(i) )^2 - n*(x-bar)^2 / n-1] ^ (1/2)
It is often less work to do the calculations the second way, but it takes a bit of thinking to get to that equations. So perhaps the first equation is the "working" way and the second equation is the "thinking" way.
Just a guess; I haven't heard this terminology before.
Tim F