This tool at Smith’s Tavern is a mortise axe. It has a long wooden handle and a steel axe head, one end of which has a thin axe blade and the other end has a larger butt end.
This is a specialist axe designed for hewing sills and notches in joints. The long narrow axe head made it easier to work on large logs. The shape enables the user to hew a long way down into the notch, where otherwise a chisel would be needed.
This tool is also hammered but more like a chisel than a splitter. The mortise axe chisels a tenon from the end of a hewn log. This tenon will fit into a mortise hole made with other tools. A mortise and tenon joint is a standard joint used when building a post and beam structure.