Are waves and surface currents the same? Why or why not?
No, waves and surface currents are not the same thing. A current physically moves water from point A to point B. Surface currents actually move matter to a new location. The actual water molecules will be carried in a single direction along with other characteristics of that "patch" of water (temperature, salinity, etc.).
Ocean waves do not result in the movement of water from one place to another. Waves move energy, not matter. The wave is the visible movement of the energy, but no matter is actually pushed in a single direction. The individual water molecules will vibrate (move in a circle) and oscillate, but they are not being transported. Currents transport water. Waves vibrate water. I've provided a link to a GIF file that has a nice animation of water wave movement.