Always wonder when woodcock are discussed.Is it the"American Woodcock"- Philohela minor ,or the "common snipe"-Capella gallinago.Different species,but somewhat similar to many observers.They are of the same family-Scolopacidae.
Given their differing preferences in food and feeding, habitat, cover, concealment, holding and flushing behavior, I'll leave the "how similar" to the observer.

NB: These were courtesy of a friend. He shot them on an epic day of mixed-bag bird hunting last fall, when he came up short on the "upland grand slam in a day" when he missed the grouse. He did get these, a nice cock pheasant, a turkey and a very befuddled dog.