Are transgender people born physically different from others?
The concept of transgenders has nothing to do with sexual organs at birth. Transgenders is a concept that has to do with sociology, not biology. See the wiki link.

intersex (previously called Hermaphroditism) has to do with biology. The wiki link makes a great job at defining intersex.

In short: A transgender person is born anatomically either male or female (with eventually exception of intersex who go on to become transgender) and they then identify themselves to the opposite sex (or a third sex) rather than identifying themselves to their actual anatomic sex.

Note that this post is closely related.