Transgender is a broad term that can be used to describe someone whose gender identity is different from the gender they were assigned at birth. “Trans” is often used as shorthand for transgender.
To treat a transgender person with respect, you treat them according to their gender identity, not their sex at birth. So, someone who lives as a woman today is called a transgender woman and should be referred to as “she” and “her.”
It is also important to acknowledge that one’s Gender identity is their internal knowledge of their gender (for example, your knowledge that you’re a man, a woman, or another gender). Gender expression is how a person presents their gender on the outside – that might include; behavior, clothing, hairstyle, voice or body characteristics. Everyone has a gender identity and expression, including cisgender – or non-transgender – people.
Other definitions/ things to note:
When a person begins to live according to their gender identity, rather than the gender they were thought to be when they were born, this time period may be called gender transition.
Some transgender people identify as neither a man nor a woman, or as a combination of male and female, and may use terms like nonbinary or genderqueer to describe their gender identity.
It is important to use respectful terminology regardless of how someone identifies. This includes using the name the person has asked you to call them (not their old name) as well as the pronouns they want you to use. If you aren’t sure what pronouns a person uses, just ask politely.