Two things that we can shoot but only do one are snipe and golden plover. In fact I don't know anyone who has ever shot golden plover. Although I have shot snipe, walked up, over dogs. But it was in Scotland about twenty-five plus years ago.
We get snipe on our shoot. There are two types in the UK, the common snipe and the jack snipe, which I believe is a winter visitor from Scandinavia and seems to turn up when the woodcock arrive. The common snipe is, um, most common and is found on marshy or boggy ground, where it feeds on insects that reside there. We have shot the occasional one. The jack snipe is smaller, but it's not easy to tell them apart in flight. Which is a problem as the jack snipe isn't on the quarry list.