In multicellular organisms, the process of differentiation produces cells that are specialized to perform specific functions. for example, one cell may become a muscle cell whose function is to shorten or lengthen to allow movement. another cell may become a nerve cell whose function is to relay signals in response to stimuli. how do the dna and genes in a muscle cell compare to the dna and genes in a nerve cell?

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.