Transsexual is a term that used to be used describe a person whose gender identity does not align with the sex they were assigned at birth. Transgender or trans is generally the more favored term. Whatever words a person tells you to use for them are the words you should use.
Rooted in clinical and medical terminology and diagnosis, transsexual differs from the umbrella term transgender and the two are not interchangeable. Transexual is mainly considered to be an archaic term, but there are some people who find it comfortable and prefer to use it.
Transgender encompasses many different experiences of people whose gender identity does not match their birth sex. A person who identifies as transsexual, however, was generally regarded to be a person who has, or hopes to alter their body through some degree of medical intervention to align their physical form with with their gender. Transsexual can be used as either a noun or an adjective, however, more commonly as an adjective, such as “transsexual man” or “transsexual woman.” Transsexual is commonly abbreviated as “TS.”
Because of its early connections to medical diagnoses of mental health concerns (and a fraught historical relationship between trans folks and the medical establishment), transsexual, as a catch-all term, has fallen out of favour in common usage. some transgender people consider the term transsexual to be offensive and choose not to use it.
Others reject it because it has a heavy alignment to surgical intervention, which is not a requirement in transgender identity. The idea that medical transition is a "real transition" is rooted in colonialism and the pathologizing of queer gender expression.
Another concern that has been raised is the inclusion of “sexual” as part of the word. Trans identity does not connect to sexual identity. Trans people’s sexual identities are varied and dependent on the person.
Those who do identify as transsexual and who do seek body modification as part of their transition, can explore many different options. These include hormone replacement therapy, top surgery, genital reconstruction surgery, plastic surgery, hair removal and more. Transsexual people can also explore gender expression through non-surgical methods, such as wearing the clothes of their identified gender, mannerism adjustment and name changes. Some transsexual people choose not to make changes, but are still transsexual.