All cells in an organism have the same origin, They come from a single fertilized cell called the zygote. Therefore, all cells in an organism have the same DNA and genes.
In order for a cell to become a specialized cell like a muscle cell or a nerve cell, it goes through a process of differentiation. Even though the DNA of the cell remains unchanged, the expression of genes in different cells differs greatly. Cell's surroundings and chemical factors trigger cell response and expression of genes specific to that type of cell.
So, the DNA and genes of all cells in an organism are the same, the thing that makes the difference is the specific expression of the genes.
