Considering that all cells in an organism's body have the same genes, what is it that allows cells to become different from each other or specialized, i. e. differentiated. (e. g. muscle cells, nerve cells, bone cells, etc.) ?

Cell differentiation is how cells become specialized. This occurs through a process called gene expression. Gene expression is the specific combination of genes that are turned on or off (expressed or repressed), and this is what dictates how a cell functions.