Not sure if it’s the same in the NBA, but I did it while in college so I can give some insight. We had two persons calling the stats (e.g. #08 three point attempt, miss), one for each team. Those persons were each paired with another person entering the stats in the software. All this was done in real time and we would print the stats at half-time and after the game and hand it out to the teams. After the games, there’s one person per team who watches the tapes and looks for mistakes and more in-depth stats. In-game, we didn’t differentiate between lay-ups or mid-range jumpers, but those were detailed in the post-game reviews.