"Transsexual person" is the medically correct term, but has recently fallen out of favour so that gender identity can be more easily distinguished from sexual orientation by laymen. Heterosexual, bisexual, pansexual, skoliosexual, and homosexual all refer to sexual orientations so the term "transsexual" can be all too easily misconstrued. The term transgender is meant to fix this issue.
Please note that all of the above terms are adjectival rather than nominal. That is, "transgender person," "transgender individual," "transgender man" (FtM), "transgender woman" (MtF), or "person who is transgender" are grammatically correct. Just as you wouldn't say "a black" you wouldn't say "a transgender," nor is "transgendered" a word.
To be clear, I'm not accusing you of making these mistakes, just putting information out there for all to see. For me it's about proper use of language and not concerns of political correctness.
Lastly, I wanted to let you know I would have upvoted this article had I seen it within the first few days of posting. Admittedly I didn't read it in its entirety, but it was obviously well researched. Being active in the LGBTQ+ community I thought I was well versed, but I certainly learned a few things. I sure wish payout periods were longer here because this article deserves five times the rewards it earned.
RE: Do Transsexual Persons Have An Opposite-Sex Brain?