Like jkarp said variations for sure. I assume Lonnie is using a "normal" mash liquor/grist ratio in his mash and then adds the "equilibrium" water. The premise in this post adds all the water at once in the mash tun. Then recirculates occasionally, and constantly during mashout. I have a very similar setup as Saccharomyces but I put all the water in my BK and dump my grain in and recirc occasionally and constantly during mashout in a single vessel.
I think the Brutus is between a "traditional" sparge and the no sparge talked about here. The "equilibrium" step as sparging to me and Lonnie even calls it a recirc sparge. He's just not lautering when he does it so I guess its not technically a sparge?
Lonnie is no sprage, and the technique Saccharomyces/jkarp/me use is Full Volume
No Sparge. Maybe to some this is a distinction without a difference. But your mash pH will definately be different with all the water in the mash. The mash will be quite thin with all the water, and have better temp stability during the mash. The temp stability might not really be a that big of a deal if your able to heat your mash tun.
You should check out jkarp's post also:Countertop Brutus 20
. He has a similar set up as Lonnie, but does a full volume mash.