Sex refers to the body (determined by chromosomes).

Gender refers to the brain.

Gender is not a social construct because men and women have typical differences in the brain.

Many gender roles and stereotypes ARE social constructs, but some of them do have a basis in men and women simply having different brains.

Intersex refers to people with bodies that do not fully allign with either sex.

Transgender refers to someone who's gender (brain) conflicts with their sex (body), which causes gender dysphoria.

For someone truly experiencing gender dysporia, trying to change their brain doesn't help. For a lot of people, the best way to reduce dysphoria is by changing the body by medically transitioning.

Some people have sexual reassignment surgery, some people only change secondary sex characteristics, and some people don't transition at all. And that's okay because they personally determine how these decisions will impact their depression and if it is worth it to them.

Are people with a female brain who were born with a male body truly women? I don't know, but society should respect their gender identity and refer to them as women because that is generally best for people's mental health.

There are people (and I have no idea what percentage this is) who claim to be trans but do not actually experience gender dysphoria and really are cis. But we should not assume this is the case when interacting with people.

While it is important to respect people's gender identity, there should be some regulations on when minors are allowed to undergo various stages of medical transitioning. Also, there are some areas (such as sports and criminal sentencing) where one's hormonal/anatomical characteristics cannot be ignored, and unfortunately trans women cannot always be treated exactly the same as cis women.

Sex, gender, and transgenderism are all real and are not merely delusions or social fabrications.