Only the market/professional "hunters" used punt guns to shoot flocks on the ground or water.
Everyone else used a regular shotgun of 4 to 12 guage with the same techniques used today.
Yes. More has been written about the market/peofessional "hunters" and their escapades than farmer Fred's or office worker Eugene's waterfowl hunting.
Also at this time over in Britian and Europe the Gentry were hunting waterfowl. For the most part, they were not shooting flocks on the ground or water, but in the air.
(I'm sure some did shoot at birds that were not flying as well, just as some around the world do today.)