What is Gender and gender sensitivity?

Your sex is whether you have male organs or female organs. Some genitals are not clearly male or female.

Your gender identity is how you accept yourself and who you believe yourself to be. You usually believe you are male, female, or some combination. A transsexual has either a male or female identity, never both as with some transgendered individuals. When a transsexual person says that their gender is their destiny, they are referring to their gender identity.

Gender role usually comes from the way your culture and society believes males and females should behave. When a feminist says that their gender is not their destiny, they are referring to their gender role.

Gender Sensitivity is the ability to recognize issues and problems in the way societies look at gender. It particularly looks at how women act and are treated and the different way that women understand their roles. It includes an understanding of stereotypes and how discrimination and gender roles hurt people, both in the past and still today. To put it into simple terms, it's not judging and refraining from being/sounding sexist, just like most people try to avoid being racist.

Further discussion/clarification:

Transsexual persons have a body that is at odds with who they really are, and their gender identity and presentation is not "varied" in any way. They try to conform to society's view of the sex they believe they are and want to be treated as a full and complete member of that sex. That is why they get surgery to feel complete and to be regarded fully as cisgendered, not trans+ anything. Transgendered persons merely live in a way that is at odds with how society says they should live, and they usually have a gender identity and/or role that is between the genders. They have no need to "correct" their body since to them, their gender presentation is at odds with society, not their bodies.