A eunuch is a man who has been castrated. it's usually applied to a man who has been castrated for non-medical reasons, and (usually) against his will.
'Transgender' refers to a person, male or female, who dresses, acts or presents in a manner that differs from his or her gender norm. 'Transgender' includes transvestites (both fetish and dual-role), drag queens, drag kings, androgynes and genderqueers. It does NOT include transsexual people.