Shot and feathers come together
Nowadays we have an apparently ever increasing variety of shotgun sports, also called "Clay Pigeon Shooting", but many of us either forget or try to ignore how the sport began.
Shotgunning as we know it today began in the later part of the XVIII century when the first practical shotguns came to light. By practical shotgun I mean a smooth bore long gun that was light enough that it could be handled relatively easily, ergonomic enough that a person could swing it while pointing at a moving target (really, a bird), and with a fast enough lock time (that is the time elapsed between pressing the trigger and the main powder charge being ignited) that would make it possible to hit a moving or flying target (again, a bird).
As widely discussed and publicized, shotguns first achieved perfection in England, and Joseph Manton is regarded as the creator of the first "Best Gun" and the forefather of the London Gun trade.
The point is that once practical shotguns were available and hunting seasons were over, people still wanted to use them, so friends began shooting at each others hats thrown in the air (but there is no historic evidence of that), but I imagine that they soon got tired of shooting at their hats, probably because it was boring and could become sort of expensive, since the beaver pelts to make those hats had to be imported from America.
So they put their hats to other use. After digging a shallow hole on the ground, and place a live pigeon in it, they covered the hole and the pigeon with their hats. A long string attached to the hat and the shooter (not a hunter anymore, but a shooter) would order "PULL" for whoever was manning the string to free the pigeon, and then shoot at it.
Apparently those shooter had plenty of old hats (at least that is my assumption as they may have shot them before the pigeons, again, no historic evidence), and they probably used those old hats, since one of the first famous Trap Clubs in England was called the OLD HATS.
After the game reached the United States of America and the passenger pigeon became scarce (that was before it became extinct), the typical American ingenuity put itself to work to find suitable replacements for live pigeons. First Captain Adam Henry Bogardus invented the "Bogardus" glass ball in 1866, and then Cincinnati trap shooter George Ligowsky created the discoid clay pigeon in 1880, and we continue to shoot it today.
From these humble beginnings (maybe not so humble, as the first live pigeon shooter apparently were either of noble blood or had enough money to spend time with them), a multitude of "Clay Pigeon" spots was created, but every single time I pull the trigger I envision my shot charge connecting with the feathers of a fast flying live pigeon against the blue sky.