A cross dresser is someone who wears clothes associated with a different sex, while a transgender person is someone whose gender identity or expression differs from the person's biological sex at birth. The term "cross dresser" often refers to a heterosexual man who sometimes wears women's clothing.
Cross dressers do not wish to change their sex permanently. The term "transgender" is an umbrella term for a wide range of people who identify in different ways. Many transgender people undergo surgery or take hormones to change their bodies, but others do not find medical procedures necessary to live in accordance with their gender identities.