In plant cells, the first part of mitosis is the same as in animal cells. (Interphase, Prophase, Metaphase, Anaphase, Telophase). Then, where an animal cell would go through cytokineses, a plant cell simply creates a new cell plate in the middle, creating two new cells.
plant cells
This is possible because proteins are created from different combinations of amino-acids. While we only have 20 different kinds of aminoacids, these 20 kinds can create thousands of combinations that we can observe in our bodies and bodies of other mammals as well as other organisms.