I'm a little confused. Could you please explain all the different genders? It seems there is so much more out there than just male and female: transsexuals, he-shes, shemales ... And are hermaphrodites real? I'm most intrigued by them. Do they live as male or as female? Are they born that way? Who's who?
OK, but you should know going in that you're setting me up for abuse from a certain segment of the genderfolk, that overearnest subset that thrives on righteous indignation. I don't know what it is about the Gender Weirdness Club that renders so many of its members both unnecessarily hostile and so shockingly humorless you'd think living as a guy in a dress, for instance, would pretty much force you to develop a sense of humor but if I talk about this, I will infuriate people, and this time I blame you. That's OK, right?
Transgender is an umbrella term. It used to be pretty much interchangeable with transsexual, but the latter is on its way out (too identified with men who went to Sweden in the early '60s and came back looking like very-large-footed stewardesses, I guess). Many people in the gender community now use the term transgender to describe anyone who does not fit readily into the "a boy is a boy and a girl is a girl, and that's that" paradigm. When I say umbrella term, mind you, I mean a really big umbrella. There's a crowd under there, from the girl in combat boots who would have been described as a tomboy in a previous generation (I was one, and it never would have occurred to me to call myself anything other than female, but fashions and perceptions change) to the aforementioned guy in a dress, with a large and oddly dressed crowd doing the Time Warp in between, including some who blur the line for kicks and others who are just trying to mess with you.
Transsexual used to be the common term, as I said, for someone described as trapped in the wrong body. Now you're more likely to hear transman (a man assigned a female gender at birth, later corrected by some combination of introspection and self-acceptance, gender presentation, hormones, and/or surgery) or transwoman (the same but vice versa). Some transfolk make a distinction between the idea of transsexuality (literally "crossing sexes") and being a (trans)man or (trans)woman: they feel they never changed genders, just other people's perception of their gender, so they don't feel a term like transsexual accurately describes them. Many would probably prefer to be known as men and women, for obvious reasons, but accept or proudly bear the trans label.
He-she is a term from the carnival sideshow. You'd probably best just file that one away with the rest of the historical oddities if you want anyone to talk to you about this.
As for shemale ... I recently pissed off an earnest transperson let's call her Ernestine merely by answering a question about shemale porn; the writer's boyfriend was nuts about the stuff, and she wanted to know how worried she should be. Not very, I said. "Lots of people enjoy blah blah blah shemale blah ..." Blam! "No transsexual woman," Ernestine wrote, "would expose her genitals like that on the Internet." She meant to convey the fact that transwomen are not freaks and need not find work at the aforementioned sideshow, a noble sentiment and all, but the fact that they are not freaks does not preclude some of them from becoming whores. There is a huge market for transporn, and much of it does use the admittedly objectionable, if undeniably retro amusant, term shemale. Sorry, Ernestine.
And finally, you asked about hermaphrodites. Nobody uses this term anymore unless they're describing worms.