A wave is travelling energy. If energy is moving outwards from a central source, you are looking at waves.
Oscillations happen when a mass moves back and forward in a regular rhythm.
Typical oscillations include a pendulum swinging to and fro, a mass on a spring bouncing up and down, a wheel on a spring twisting clockwise then anticlockwise - even the tide flowing in and out of the harbour mouth. Quite often, waves and oscillations are part of the same thing. Energy is spreading out over the whole pond - so there are waves in the pond. At any one point on the surface, a mass is moving in a regular rhythm - so there are oscillations at that point.