Cells are the most irreducible "building blocks" of life. They are microscopic in size yet possess every fundamental property that signifies life itself, including metabolism and reproduction. When the cells that belong to prokaryotic organisms reproduce, these simple, organelle-free cells divide by a process called binary fission, and two new daughter cells (and usually, whole daughter organisms) result.
Eukaryotic organisms, in contrast, are more complex and have a cell cycle, which ends with two division steps: Mitosis, which is the division of the nucleus and its contents, and cytokinesis, which the the division of the cell as a whole. These consecutively occurring phenomena are easy enough to tell apart given basic familiarity with both processes.
The Cell Cycle
Mitosis and cytokinesis lie at the very end of the eukaryotic cell cycle. This cycle includes an interphase, accounting for the vast majority of a given cell's life span, and an M phase, which is simply another name for mitosis plus cytokinesis.
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Interphase represents the part of the cycle in which the cell is preparing to divide but not yet actually dividing. It includes three steps of its own: G1 (first gap), S (synthesis) and G2 (second gap). Cells make copies of their chromosomes in the S phase.
The M phase includes mitosis, which is the reproduction of the nucleus and its contents, and cytokinesis, which is the cleavage into daughter cells of the cell as a whole.
Mitosis itself is the division of the nuclei into daughter nuclei. It includes five phases of its own.
Prophase: Here, chromosomes become more condensed in the nucleus, and the nuclear membrane dissolves. The mitotic spindle forms from the centrioles, which have split and moved to opposite poles (sides) of the cell. This spindle is made of proteins in the form of microtubules.
Prometaphase: In this step, the chromosomes migrate toward the center of the cell. They are propelled by the mitotic spindle apparatus attached at the centromeres that joins sister chromatids. They begin to approach a line perpendicular to the direction they are moving, through their centromeres, called the metaphase plate.
Metaphase: In this step, chromatids align precisely along the metaphase plate via their centromeres, with one sister chromatid on each side of the metaphase plate.
Anaphase: In this step, the sister chromatids are pulled to opposite poles of the cell, releasing from each other at the centromere. The spindle fibers, again, are responsible for this motion.
Telophase: In this step, daughter nuclear membranes form around the newly formed daughter nuclei. At this point, chromatids are unpaired, as this generation's chromosome replication has yet to start. This is because cell division is not quite complete.
To define cytokinesis as a stand-alone phase, the difference between telophase and cytokinesis is best imagined by thinking of telophase ending the instant both daughter nuclear membranes are completely formed. Cytokinesis starts with a "pinching inward" from the top and the bottom of the cell, with one daughter nucleus on each side.
This "pinching" results from the formation of a protein structure called the contractile ring, which runs around the widest part of the cell under the membrane. When this shrinks inward, it pulls the membrane tighter along with it until the cell halves are completely separated by the now-finished "pinch."
Mitosis and Cytokinesis Overlap
Cytokinesis begins after mitosis begins and is completed only after mitosis is completed. However, the two phases do overlap, as the cell itself formally starts the division process during anaphase of mitosis. This makes physical sense, when you think about it: Only after chromatids completely separate in one direction is it "safe" for the "pinching inward" of the cell to occur along a plane between those chromatids.