Would a nerve cell and a blood cell from a human contain the same DNA

Every cell of the body contains the same DNA. So, the nerve cells and the blood cells have the same set of genetic instructions.

Different cells are produced by differential use of that DNA. Different sets of genes must be turned on and off in the various cell types (differently expressed genes).

Most cells in a human body contain a complete set of the genome (the genetic material of an organism), which is two sets of 23 chromosomes, with exception of egg and sperm cells, which carry only half a set of chromosomes (23 instead of 46).