I've always been pretty firmly of the belief that gender identity - like sexual identity - is pretty much a social construct. I was born female, and still am, but have been told that I have a lot of "male" character traits. I don't agree - I have my own character traits, and they're neither male nor female, they're just me. Similarly, I've always been in relationships with men, but I think that it's just been that - so far - the people who I've been attracted to have been male. So I do agree with MrsTerryPratchett that if gender identity wasn't an issue for society, it would become less of an issue for the individual.
However, DC2 identifies as a gender other than his birth gender (I apologise for any offence I cause here by using male pronouns to discuss him - we've discussed this and he is completely happy at the moment with me using these, rather than gender-neutral pronouns, but I know that many trans people do prefer the use of gender-neutral words). He says that he originally identified as a gay man (he came out to me when he was 13 or 14) but more recently thinks that he'd be more comfortable in his own skin living as a woman (and decided this at the age of around 15). He says that it wouldn't make much of a difference to him whether or not society sees him as male or female, or if society didn't give a stuff either way, because what matters is how he views himself.
He doesn't have particularly "feminine" personality traits - I've asked if he'd like to have more typically female clothes to wear about the house, for example (to which he responded by looking at what I was wearing and said "so that'd be jeans and a t-shirt, then"). He says that he doesn't particularly want genital surgery, but wants hormone treatment so that he doesn't grow a beard, and so that his body (other than his genitals) becomes more "female" - in terms of fat distribution, skin texture, growing breasts. So even within trans people, there seems to be a continuum of identity, rather than a definite "I'm this gender, and I want to be that gender, with all it entails".
Sorry for the rambling, it's a bit early in the morning for me, but I think that it's worth saying that the differences between two trans people can be as marked as the differences between a trans and non-trans. Everyone is an individual.