Transsexual is an antiquated term used for someone whose gender identity/sex does not match their sex assigned at birth. As explained by the Gender Equality Law Center, someone who is “transsexual is a person who identifies psychologically as a gender/sex other than the one to which they were assigned at birth. Transsexuals often wish to transform their bodies hormonally and surgically to match their inner sense of gender/sex.”
The term transsexual would be used for those who wish to transform their bodies hormonally and surgically to affirm their gender identity. One can identify as transgender with or without ever hormonally or surgically affirming their gender identity.
[Last updated in September of 2021 by the Wex Definitions Team]