This process is called differentiation.
Step-by-step explanation:
We know that during sexual reproduction, the mating results in fertilization between sperms and ova with production of zygote. This zygote is a single cell, which divides for thousands of time to produce a whole multicellular organism.
Each and every cell which is produced from the embryo have the same DNA and the same number of genes. But during the intrauterine life of the embryo, some cells start expressing some gene while others the different genes. This paves the way for organ differentiation and tissue differentiation. So the process by which the different cells of a multicellular organism expresses different gene inspite of having same DNA is called Differentiation.