Different cell types develop in a multicellular organism because each cell has its own unique set of genes.

That question is confusing. Cells obviously take from its parent cells, which means that DNA is combined from both mom and dad in a unique way. That can cause the offspring to have either the mom's or dad's eyecolor. So the "different genes" part apply to that because for each feature of the offspring it is a complex combination of mom and dad. What I don't get is the different cells. there are these things called stem cells which are basically cells that can be anything in the body when there's a need for it. A stem cell can be a nerve cell or muscle cell for example. So i don't think it requires genes to be exact to form a cell. I hope you get what I'm trying to say