Well, I can't help you classify the protists, because you didn't list them, but I can explain the bigger idea so you can do so yourself.
The difference between phytoplankton and zooplankton is the mode of gaining nutrition. Specifically, phytoplankton, or plant-like plankton, get nutrition by doing photosynthesis. Hence phytoplankton can be identified because they have chlorophyll and chloroplasts.
Zooplankton, on the other hand, do not do photosynthesis and must get nutrition by feeding. They are animal-like, and they may be primary consumers, eating phytoplankton, or they may be secondary consumers, eating other phytoplankton. They do not have chlorophyll, but are generally equipped with some sort of feeding mechanism and are usually more mobile than phytoplankton.
Plankton in general are generally defined as those organisms that float with the ocean currents and move with the wind. Phyto refers to plants and the ability to photosynthesize, zoo refers to animals. So, phytoplankton are plankton that can photosynthesize and zooplankton are the animal like plankton, such as the larval forms of muscles or clams, etc.