Let's say there's a sample stock, XYZ, that trades on NYSE (or maybe NASDAQ). I can look at the historical data for it (from any number of websites) to see its volume and OHLC data for any given time period, down to the individual minute.
But what I want to see is a list of all the trades that actually occurred during that minute, with the price and quantity of each one, and possibly even which broker/market maker was involved with the trade. Presumably the exchanges themselves have a detailed record of every trade they've ever executed, but I imagine they don't provide this information to the public (or at least not to retail investors like me). (I've been led to believe that sometimes trades are executed within a broker if the broker has two clients whose orders match up, and such trades never actually go to the exchange.)
I know order books are a thing, but it's my understanding that they only show pending orders, not a list of completed transactions.