in semiotics, a trace is the physical and material result of poietic processes, the "message" made by a "producer" and interpreted by esthesic processes of a receiver.
in linguistics, a trace is a notional "ghost" of a syntactic entity that can be regarded as being in an utterance for the purposes of syntactic analysis.
in transport, a trace is one of two, or more, straps, ropes or chains by which a carriage or wagon is drawn by a harness horse or other draught animal.