How can the cells in a multicellular organism differ from each other when they all have identical DNA

Well, they serve different purposes. Depending on the type of cell, different cells are affected by different DNA. Stem cells can become any cell type, and are extremely abundant in developing babies. Think of it like the clones in Star Wars, all the same DNA, different jobs.

Well all cells in a multicellular organism have the same exact DNA (except for sex cells). But what makes each type of cell different physically and functionally is the genes that are expressed in those cells. So for like example a different section of the DNA molecule is expressed in a nerve cell than a skin cell.