Hi Sunrise.
Lets start with Transgender. Transgender(TG) is mainly used as a all encompassing umbrella term, that includes but not exclusively, Transsexuals, Transvestites and Gender Queer.

Transsexual means someone who is gender dysphoric, i.e a bio female feels (knows) on a very deep fundamental level that they are a man, and vice-versa for male to females.
To use a simile, it's like handedness. I know i'm left handed, as i was born that way. But if i lived in a society where left handedness was frowned upon and i was coherst(sp?) to use my right hand, i would still be left handed not matter how pressure was brought to bear to say that i wasn't. It is a instinctive trait of who i am.

I hope i've made sense, as it is past 2am and last night i only had a couple of hours sleep!! O_o