Ok. Did a bit of reading and answered my own question.
Seems like Mainlining was first, started by a grower named Nugbuckets. His technique was to top the plant producing two opposite branches. Then he topped those two to produce four, and topped the four to produce eight colas. Each cola is the same distance from the roots in this method.
Then, a grower named Nebula Haze took that idea and eliminated the additional toppings and just let the original two branches grow and used the side branching to make up her eight branches, claiming to have saved a bit of veg time in the process with no loss of yield. This was termed "Manifolding."
Then
@Light Addict came up with his more elaborate, and time consuming, training more along the lines of the second version, but focuses more on creating many, many more tops than the eight found in either of the two prior versions, with a bit of weaving of stems along the way. LA calls this technique "Fluxing".
And from there we now have
@Asesino85 's quadlining version which tops but leaves four branches to grow instead of two, shortening veg time even further and producing a very symmetrical plant.
I think I have my history right but am happy to be corrected if anything is not accurate or complete.