A wave pulse is a disturbance that moves through a medium.
A periodic wave is a periodic disturbance that moves through a medium. The medium itself goes nowhere. The individual atoms and molecules in the medium oscillate about their equilibrium position, but their average position does not change. As they interact with their neighbors, they transfer some of their energy to them. The neighboring atoms in turn transfer this energy to their neighbors down the line. In this way the energy is transported throughout the medium, without the transport of any matter.