The adzes with with tapered spike are called ship carpenter's adzes. The spike is for countersinking nails below the decking material. You may also occasionally find a carpenter's poll adz that has a hammer type poll on it instead of a spike.
The most common types of regular adzes are the flat head, the half flat head, the poll adz, and the ship carpenters adz. There are also cooper's, gutter, connecticut hand, ice, railroad, lipped ship carpenter's, bowl, and others.