A single cell organism is called a microorganism. A microorganism is neither an animal or plant. Some examples of microorganisms are protozoa and bacteria. These single cell organisms are some of the most important life forms on Earth.
A single celled organism is usually referred to as unicellular. Most of the single celled organisms are usually microscopic and are mostly bacteria. Robert Hooke is credited with discovering the cells in 1665, setting the stage for research in cell theories.