Readers know that I no longer seek to shoot Woodcock anymore, but I sure don't mind people who do. Tasty little critters but for me kinda sad to hold one in the hand.
Woodcock are odd birds, basically shorebirds who ended up as upland birds. They still like soft earth and water, though. Swamps. I love to see them.
Here's Understanding the Fall Woodcock Migration
The European Woodcock is larger, probably more worth shooting. I do know, first hand, that the Irish like hunting them.