Mitosis and meiosis are the two types of cell division, with mitosis producing somatic cells and meiosis producing gametes like sperm and egg cells. Mitosis results in two identical daughter cells through prophase, metaphase, anaphase and telophase, while meiosis reduces the chromosome number through two divisions, meiosis I and meiosis II, resulting in four haploid cells. The stages of each type of cell division involve chromosome condensation, alignment, separation, and decondensation along with cytoplasmic division.