In the case of lap winding, the end of a wire conductor is connected to the commutator, then the other wire end is connected to the beginning of the next coil segment. This winding configuration refers to the fact that the wire "laps over" each segment as the winding structure reaches its terminus.
With wave winding, one wire conductor is wrapped under one pole, then connected to the back of the next pole. In this case, the series of wire conductors do not directly overlap, but when it's completed, the structure looks like a series of copper "waves" wrapped around the commutator.
Non-lapped winding refers to a wire process that does not employ overlapping at any point across the commutator but employs a linear side-by-side configuration from the front to the rear of the structure.