"Plankton" is the term that generally refers to the "floaters," the organisms in the ocean that drift with the currents. This includes zooplankton ("animal plankton"), phytoplankton (plankton that are capable of photosynthesis), and bacteria.
Plankton are at the mercy of the wind and the waves, but not all are completely immobile. Some types of plankton can swim, but they swim only weakly or vertically in the water column. And not all plankton are tiny - jellyfish (sea jellies) are considered plankton.
Some marine life go through a planktonic stage (called meroplankton) before they are free-swimming. Once they can swim on their own, they are classified as nekton. Examples of animals that have a meroplankton stage are corals, sea stars (starfish), mussels and lobster.