Based on the data that I have seen so far, the definition of transgender is a popular search term. However, most of the results are from dictionaries or from people who are not themselves transgender. As a transgender woman, I have thought a lot about this and would like to attempt explaining this to you. Let's try to arrive at a definition of transgender, and the relationship between the word transgender and transexual.
Before we attempt the definition of transgender, let's talk about birth sex. It is the sex of an individual at birth. It relates to the genitals or sex characteristics they are born with. Therefore, someone born with a penis is Assigned Male at Birth (AMAB) and someone born with a vulva is Assigned Female at Birth (AFAB).
It is worth noting that people born with sex characteristics that don't fit the male or female binary are intersex.
Gender and Gender Identity
For the longest time, people equated gender with birth sex. Anyone born with a penis was a man, and anyone born with a vulva was a woman. However, our current understanding is that gender is much more complicated than that. It is also not binary but instead it is a spectrum.
Gender identity is a person's sense of their gender. It is independent of their birth sex and can only be defined by the person themself. It is what they feel.
What is Cisgender?
More often than not, a person's gender identity aligns with their birth sex. It is so common that it is tempting to call that normal, and anything else queer. The better word to define such people is cisgender. To illustrate, if you were born with a penis, and you identify as a man, you are cisgender.
What is transgender?
As you can probably guess by now, there are people (even though a minority) who don't identify as their birth sex. These people are transgender. It doesn't mean that there is anything wrong with them - they are definitely not mentally ill or strange.
For reasons that are far too complex for me to explain, we, transgender people find ourselves in this situation. It causes a lot of us severe mental discomfort or dysphoria and some of us may decide to transition to the gender we identify to alleviate it. However, whether we transition or not has no bearing on us being transgender. It's worth reiterating that we only choose to transition. We don't choose to be transgender, much like many don't choose to be a cisgender.
Another thing worth noting is that not all transgender people identity as male or female. Many of them fall outside of the binary. Gender identity is personal, immutable, and can only be established by the person. No one else has a say in it - not the family, society, and definitely not the government.
What is transexual?
I must confess that my understanding here is pretty limited as well. I started transitioning in 2016 and I met several transgender people who absolutely detested the word transexual and therefore I never really used it. I encourage you to research on your own and decide for yourself.
There you have it - my attempt at explaining what is transgender. If you have any comments or suggestions for me, I'd love to hear them on Twitter.