Are you in a blended family, how do you view the kids?

If you are in a blended family (with kids from prior spouses), how do you view the kids? If your spouse has kids and you don’t do you view them as his kids or as yours as also? Does the spouse see their kids as yours also? What if both of you come into the union with kids, is it his/her kids and your kids, or are they all the both of you kids? Is your spouse comfortable with you punishing or admonishing the children they are parents to the same as you would your own children and vice versa?