Cells are either eukaryotic or prokaryotic. Both plant and animal cells are eukaryotic. Prokaryotes are unicellular organisms, but it is worth noting unicellular eukaryotes also exist (Protozoa). Eukaryotic cells contain membrane-bound organelles (such as the nucleus) while prokaryotic cells do not.
Plant cells have a cell wall while animal cells do not. This gives plant cells a rigid shape while animal cells are more flexible. Plant cells have organelles called chloroplasts that perform photosynthesis. Both plant and animal cells have organelles called mitochondria that perform cellular respiration.
Like plant cells, most prokaryotes also have a cell wall. It is chemically distinct from plant cells. Some prokaryotes also perform photosynthesis. Instead of chloroplasts, they have chlorophyll pigments embedded in their plasma membrane to perform the process. Prokaryotes are the smallest living organisms.