Both animal and plant cells are eukaryotic which means they have a defined nucleus. One of the primary differences is that plant cells have a cell wall made up of cellulose. This helps the plant cells to allow pressure to build inside of it without bursting. A plant cell has to be able to accept large amounts of liquid through osmosis, without being destroyed (or bursting). An animal cell does not have this cell wall and would eventually pop if filled with too much water or other fluid.