One, technically crossdressers are transgender.....especially if you are out in public as the other gender. Transgender is basically an umbrella term for varieties of gender expression, including drag queen, and transsexual.
Two, Transsexuals are also transgender but transsexual people are really cisgendered....but just not in the body they're born with.
There's a well known joke in the transgender community, it goes like this:
What's the difference between a crossdresser and a transsexual?........answer: two years!
Two years typically refers to the process of changing from male to female, or vice versa. MTF requires hair removal, hormone replacement therapy, and surgeries of one wishes, or can do so. I have a couple of close friends who have done so,and I stand on record of saying that the results are miraculous in their cases. it typically takes about two years or so.
There are also situations where one comes out as a latent crossdresser, and two years later just says, I want to be a woman. .
I have met trassexuals that hate the term transsexual, and prefer to use transgender, and are mad that crossdressers also identify as transgender simply becasuse they hate the word transsexual.