Something in between the decision makers and the guys on the floor of the exchange.
Basically the old model was that there would be a big money manager, say it was at Fidelity. He decides he wants to sell AA and buy AMR. He has a salesman at Goldman Sachs whom he calls and says to do the trade. The salesman calls the cash equity trader. Because it’s such a good customer, maybe the the trader tells the salesman that the trade can be done at certain prices, but he does not go into the market with the transaction, he holds onto both positions, GS is now long of AA and short of AMR. It’s up now to the cash equity trader skilfully to get out of both positions at profitable levels using either Goldman’s sales force, or by trading into the exchanges.
That’s as recent as 10 years ago.
Today, pretty much none of that would happen. Fidelity has its own computers, and its own access to all sorts of off-market exchanges. There, using algorithms to disguise their interest (buy v sell) and the size they want to get done, Fidelity can execute those trades very efficiently without anyone front-running the order and only paying a tiny commission relative to what Goldman would have taken back in the day.
Lots of markets are working this way now. The NYSE conducts a relatively tiny percentage of all trades in NYSE listed stocks.
Sounds like you and I were in parallel universes in the late-90’s through 2000’s! I was with a tech company that was automating those trading processes for the buy-side - particularly the trading network from them to their sell-side counterparts. It was obvious (to me) that this was all going to be automated, but the sell-side players squealed like stuck pigs. They just couldn’t imagine being displaced by computers. They were absolutely convinced that they added so much value to the process that they could never be replaced.
Some sell-side firms lived in denial, and died off. Some immediately embraced automation - and the good ones got bought up by the big Wall St. firms (like Goldman). It was a wild time!