Body waves travel through the heart of the earth while surface waves are confined to the eath's crust. Body waves travel faster than surface waves and also follow a straighter, and therefore shorter, path than the crust provides. Body waves are divided into P and S waves. P vibrations are longitudinal. Another way to think about them is that they push and pull in the direction they travel.
S waves are transverse.
They shake the ground perpendicular to their direction of travel. Their motion is similar to ocean waves and vibrations of a guitar string. Their signature on the seismograph is more rounded and of larger amplitude than the P. You can find your distance from a quake's epicenter using P and S wave arrival times. Compute the difference in P and S arrival times. Then, look up the difference on an arrival time chart to locate your distance in degrees.