They sound like the same thing, right? They're not, actually. Transgender is when your mind and soul do not match the body you were born in. Transsexual is basically when a transgender person has gone through the surgery, and already changed their body to fit their mind better.
Examples of transsexual:
"I was born in the wrong body, but now I have the proper body parts, and I feel more like myself."
"Ever since I started my transition, my hormones fit me better, and I feel more like my real gender."
So thanks for reading guys, I appreciate it :) Next Sunday's entry is about trigender and bigender.