The first two stages of a "Kosher" Bris include the removal of the foreskin and the removal of a mucosal membrane which is present directly below the foreskin.
Milah is the act of circumcision, which specifically targets the skin of the foreskin.
Priah (uncovering) is the act of the removal of the membrane.
While Milah is virtually done the same way by most practitioners, i.e. with a knife (though see below), Priah is done differently by varied practitioners, because some aim for what's called "Milah U'Priah B'vas Achas" (essentially doing both actions in one action), while others aim to make them separate actions. (see below as well)