The type of wave that vibrates from side to side and up and down is called S waves (secondary waves). S waves are a type of seismic wave that move through the Earth during an earthquake. They are characterized by their transverse motion, meaning they move perpendicular to the direction of the wave's travel, which causes the ground to shake side to side and up and down.
Surface waves, on the other hand, travel along the surface of the Earth and tend to have complex motion, typically involving both vertical and horizontal displacements, but they are not specifically described as vibrating in a simple up-and-down or side-to-side manner like S waves.