No, the terminology got simplified which made the actual meaning of Transgender unclear. Theoretically, Transgender is supposed to refer to expressed gender differing from sex (includes all nonbinary people; difficult to apply to non-humans), while Transsexual refers to the desire to permanently transition to a different sex (may be applicable to some, but not all, nonbinary people; hermaphroditic animals can sometimes be defined by this term), but nowadays people just use Transgender for both meanings.