The square faced hammer looks like it maybe a slater's hammer to me. For doing slate roofs. The longer pointed claw used for punching a hole in the slate for nail.
Could be... It looks quite different from those I'm familiar with. Those slaters hammers are called zax, and are usually a single forging, handle and head, with a wood or stacked leather grip. See attached photo.
This is almost certainly a Continental hammer, whatever its use. I have one nearly identical, except for that long, pointed claw.