There are 206 bones in a man's body and 208 in a woman's because they've also got a couple of floating ribs. As for how many different bones, I suppose you'd just half each number, as the bones on one side of the body are naturally the same as their counterparts on the other side.
Men and women have the same number of bones,. The story about women having an extra rib is a myth with biblical origins. At birth humans have about 300 bones, which reduces to 206 by adulthood largely due to fusion of bones in the skull and spine.