First, don’t say “transgenders”. Nouning-the-adjective places the category above the person. Say “transgender women/men/people”.
Transgender is an umbrella term that includes all significant deviation from the norms of gender and sex. Drag queens, transsexual people, cross-dressers, transvestic fetishists, people who identity as trans-masculine or trans-feminine, people who are genderqueer, etc. are all included.
Transsexual refers specifically to people who permanently transition from one sex to another, usually through one or more medical treatments such as hormone replacement therapy and/or genital reconstruction surgery, usually along with legal and social changes such as change of legal name and documentation, alternate gender presentation (clothing, make-up, etc.), voice training and so on.
The adjective “trans”, as in “trans woman”, usually means transsexual but sometimes means transgender. It’s usually clear from context. This article, for instance, has been about transsexual women.
Drag queens are men (typically but not always gay) who dress in an exaggeratedly, campily female way for the sake of performance or entertainment. There is typically very little emphasis placed on actually passing as female but instead on having a particularly ostentatious and fun outfit. This is an act of playing with gender roles, not an act based on expression of a deeper internal sense of self. A drag queen adopts a female persona but will (almost always) have a male gender identity.
Cross-dressers are men with a male gender identity who, for a variety of possible reasons, choose to occasionally dress in women’s clothing and accessories and present as female. The acts of cross-sex presentation are temporary and do not reflect their “true self”.
A transvestic fetishist is a cross-dresser who does so for sexual motivations, due to being aroused or getting an erotic thrill from the cross-sex presentation. They also maintain a male gender identity and the cross-sex presentation is temporary.
These distinctions are important. Seriously.