The winds that cause one cause both. Wind blowing over water causes water to move as a result ofdrag (basically friction in fluids). The drag builds up heights of water that then collapse under gravity, and the movement goes in the direction of the blowing wind as a result of its continual "falling" through the pressure gradient caused by the wind. This is what waves are. Drag from air motion also moves the surface en masse, which of course drags water below the surface with it, in the direction of the wind. This is what currents are.

On small space and time scales winds can produce surface waves; over larger space and time scales wind blowing over water will also produce a net flow or movement of water, this is called current.

Often in the open ocean far away from land the wind will blow in the same direction at the same intensity for long periods of time. Examples of these sustained winds are the North-East Trades in the sub-tropics and the Westerly in the mid-latitudes.These long sustained winds tend to push water causing water to pile up. As the water piles up some parts of the surface of the ocean will be higher than other parts of the surface of the ocean. But the ocean wants to all be at the same height, or at equilibrium, so water begins to move from the parts that are higher to the parts that are lower. This movement is the ocean currents.

Since the winds last for long periods of time without changing much, the spots on the ocean that are high and low are maintained, so water has to continuously be moving from the high regions to the low regions and the currents become fairly permanent. One example of theses currents is the California Current, which runs south along the West Coast of the United States from Washington to California.

All winds produce waves on the ocean surface and small currents in the surface layer of the ocean but long sustained winds are required for the formation of ocean currents.