I looked it up:
Ghost Story, page 199, e-book:OK, it's not so much difference. " better" - "brighter", but...
Could be misremembering from Butcher's side, but with the comment about having been there as a ghost and not at the end of Skin Game, I'm not so sure.
Oh. Wow. Good spot. It's "Brighter Future Society" in Skin Game as well as Ghost Story, and in most of the references in Peace Talks. It's *just* the plaque that is wrong, not the text anywhere else.
"My comfy, dumpy old apartment was gone, flattened by Gentleman Johnnie Marcone to make way for his stupid little castle and the Bigger Better Brighter Future Society."
"The fete was being hosted at the Brighter Future Society's headquarters..."
"But as I approached the front door, I was struck by two things: First, a modest, plain bronze plaque fixed to the wall that spelled out the words BETTER FUTURE SOCIETY in letters an inch high..."
Ramirez reads the "Better Future Society" plaque and there's some discussion. And then later, when they talk about how Murphy is familiar with the building, it's back to Brighter Future Society twice.
You're definitely on to something, and I don't think it's a timey-wimey mirror mirror thing. For some reason, Marcone stuck a plaque on the door with the wrong name for the Peace Talks. Somethine's going on -- whether it's supposed to keep the low-key paranet-level BFS from attracting Accords-level notice or foil internet searches for them, or something weirder to do with the power of true names.
Perhaps it's Brighter Future Society when Butters and the wolves and the paranetters are the face of the organization, but Better Future Society when Marcone is? Possibly there's even a third name for when it's Lara's people.
But that sure looks like a deliberate switch, especially with that "... Bigger Better Brighter..." line to prime us to miss the difference.