What kind of hammer is this

Your picture does not show it particularly well, but I believe that you have a claw (for pulling nails) formed by the "stub" and a protrusion from one side of the "spike" on the illustrated hammer.

Here's a half-decent picture from a slate supply place.

This tool is used for spreading tile adhesive (or a mortar base). The large teeth are for floor tile and the small teeth are for wall tile. If kept clean, it will last a lifetime!