Yes They do. They have entirely different chromosomes. All DNA has the same 4 chemical bases but the way it is sequenced is what gives us the incredible variety we see around us. Not only do men and women have different genes, one of the 46 chromosomes all humans posses is entirely different.
You’re speaking as though DNA, genes, and chromosomes are all the same thing. Are you seriously telling me you can take a strand of DNA and identify is as male or female?