These tools at Smith’s Tavern are a carpenter’s wood scribes, which are entirely made of wood - including the wooden screw tightener. It was used to measure and score wood. If there were ever numbers on the stick, they are illegible now. The wood being measured would be marked by scratching the surface visibly.
These tools are also called a marking gauge or scratch gauge and were used in woodworking and metalworking to mark out lines for cutting and other operations. The purpose of the gauge is to scribe a line parallel to a reference edge or surface. The gauge consists of a beam, a headstock, and a scribing or marking implement, typically a pin. The headstock slides along the beam and is locked in place by a locking wooden screw. The marking implement is fixed to one end of the beam (note the small appendage on the Smith’s Tavern tool).