Coral reefs don't fit into either category. Plankton drift with currents; nekton swim actively against them. Corals are sessile—permanently anchored to the seafloor.
What we call a "coral reef" is actually a colony of thousands of tiny animals called polyps, each secreting a calcium carbonate exoskeleton. Over generations, these skeletons accumulate into the massive, complex structures we recognize as reefs. The living tissue is a thin veneer atop a mineral foundation built by ancestors.
So while reefs teem with plankton and nekton—fish, crustaceans, larvae—the reef itself is a living geologic formation, not a free-floating or free-swimming organism.