The first picture is called a dresser while the second one is called a vanity. It's not really a drawer, but more of a dressing table used to apply makeup, do hair, store feminine products, and such.
To tell the difference, dressers only have drawers used for storing things; vanities have mirrors on top in which you sit in front of. In addition, vanities are more of a piece of furniture―typically for women―used for the things listed in the beginning, while dressers can function to hold anything, anywhere for any person. ^.^