Tides
The distinguishing factor between a tide and a current is the direction of movement. A tide moves up and down, rather than side to side. Tides are caused by the position of the sun and the moon and their gravitational pull.
Currents
A current describes the motion of water and moves horizontally from left to right as opposed to vertically. Tides are affected by gravitational pull, and the formation of a current is a direct effect of a strong tide. Currents can also be dictated by wind and thermohaline circulation.
Tidal Current
A tidal current--the combination of the above terms--is a specific type of current. A tidal current involves the horizontal movement of a typical current, but is specifically associated with the rise and fall of the tide.