Both are used to drive or remove nails. Finishing hammers are those with smooth faces. You will also be using the following Tack hammer. This is useful for driving tacks and brads. Some have magnetic heads.
Ball peen hammer .
The face of this hammer is rounded, with beveled edges. The other end is a ball-shaped peen for metal working. These tools are used primarily for striking other objects, notably chisels, or to form sheet metal. This is necessary for heavy work on concrete, or for wood splitting in conjunction with a wedge. This device, used with a hammer, is for pushing the nail below the surface of the wood when you don't want it to show.