The two main types of waves are body waves and surface waves. Body waves can travel through the earth's inner layers, but surface waves can only move along the surface of the planet like ripples on water.

Body Waves -
arrives before the surface waves emitted by an earthquake. These waves are of a higher frequency than surface waves. (Traveling through the INTERIOR OF EARTH)

Surface Waves - are of a lower frequency than body waves, and are easily distinguished on a seismogram as a result. Though they arrive after body waves, it is surface waves that are almost entirely responsible for the damage and destruction associated with earthquakes. This damage and the strength of the surface waves are reduced in deeper earthquakes. (Traveling only through the CRUST)