While watching a pesting video (don't you just love those?) I was curious about a couple of things. So I posted a comment to the video asking him and he was kind enough to answer. (most air gunners are very responsive to viewers!) He carried a satchel and referred to it as a "game bag". I use an old backpack and put my critters into plastic shopping bags as I had no idea there was something specifically designed for the job. Also, he was shooting an HW97 which, as you might know, is an under-lever single shot which he was reloading very quickly from something around his neck.
So, nosy guy that I am, I asked him about them. I thought that I'd share his answer with the community, "The game bag is really just a shoulder bag used by shotguners mostly to carry shot game in as they make their way through cover when rough shooting and the pellet holder is something i made myself years ago from an old rubber boot."
Look at that. I learned something new today, which makes it an outstanding day!
Here's his video on making that pellet holder: https://youtu.be/yuRC3n4K3-s