In other words, a person who was born with a female body, who decides to become a man, is then male. A person who was born into a man's body and then decides to become a woman, is then female. But when we are aware that someone is making a specific choice about their gender identity, we should honor that. People have the right to be self determining. The second meaning of trans is across, as in transcontinental.
Some transgender folks cross back and forth between genders.
Maybe they are comfortable being male for the most part, but occasionally like to wear women's clothes. Maybe they have a female body and identify themself as male, but don't feel the need to change their body to move across that gender line. Cross-dressers would fit under this definition of trans. This includes anyone who likes to wear clothing that our cultural norms assign to the other gender. Most people who cross dress are not expressing a desire to be that other gender.