Transverse and longitudinal waves differ only in the direction that the medium moves relative to the direction of transmission on the energy and in the names of the points of maximum amplitude. The behaviors and properties of the waves are still the same. They both travel through a medium, they both move energy from one place to another without transporting mass.

Adapted from: tpecp61, ScienceZine

For a better look at the difference, click on the following link to view wave animations.

Longitudinal and Transverse Wave Motion