Both Plant and animal cells undergo cell division. In-plant mitosis, cell division in induced by a plant hormone known as cytokinin. The process occurs in the meristem. The shape of the cell does not undergo any form of change. Mitosis apparatus in plants lack asters and spindle is ancestral.
It also lacks centrioles. Animal cell become rounded before cell division starts. There is no specific known hormone that induces mitosis. During the process, centrosomes are formed. Mitosis apparatus in animal cell division consists of asters. Spindles degenerate before the beginning of cytokinesis, and it also occurs throughout the body.
Plant and animal cells would need to undergo cell divisions. The only difference between the two is their ability to form daughter cells during cytokinesis. Animal cells will usually form a cleavage that will ensure that the daughter cells can be created properly while plant cells will not form any furrows because of the cell wall.
Cytokinesis occurs in both cells but this major difference will make you realize which is which. There are some people who may assume that the cells are inactive during some of the stages but they are just bracing themselves for the stages that will occur that will ensure that the process will be complete.