Nearly ten years ago, a therapist first suggested to me that I was transsexual. I did not deny it, but said I was too old to transition.

The truth is, back then I could not handle the idea of transitioning. It seemed like too huge a step, whether or not I ever had GRS. I also told him I was too old. Times change.
When I started gender therapy at the University of Minnesota Program in Human Sexuality, ranked as one of the top or the top programs in the country, I was diagnosed with Gender Identity Disorder (GID) after two visits. I told my therapist on the first visit that I thought I was probably asexual (i.e., eunuch) in gender identity. I absolutely knew I did not feel male. She had no problem with this as a type of GID. [She did not choose to use Gender Identity Disorder Not Otherwise Specified.] The U of M is at the forefront of much of the thinking and study on GID and transgender persons. Their view point is that gender is not bipolar, either masculine or feminine, but a continuum. It was only after a month or so in the program, with time to think and explore, that I began identifying as androgynous. Shortly after that, I was saying I had leanings toward the feminine end of the continuum. It was at least two months after I started the program before I had the courage to state that I thought I was transsexual. I never felt pushed toward one identity or another by my therapist. She urged a very cautious approach before making decisions on treatments that have, after a time, irreversible effects.
My U of M therapist made a very interesting point that is pertinent to this thread. They were continuing to learn a lot about the variety of gender identities and expressions from their clients.
DSM-IV was published in 1994 and, although it is still used for diagnostic purposes, there has been a significant change in how Gender Identity is viewed since then. A new version will be released in 2012. I think a preliminary draft will be available later this year. There is a lot of controversy about how GID will be addressed in the new release.
Having a diagnosis of GID does not, in itself indicate that one is transsexual. Even if you adhere to the stricter diagnostic criteria in DSM-IV rather than the U of M interpretation, there is still room for variation in gender identity and expression. A lot of this is semantics, in my view, and of little interest outside of therapy and an examination of medical treatment options.
I don't have time to investigate this further, but there is a tendency to label those who wish to live as the gender 'opposite' that of their birth as 'transgenderists' if they have no desire for surgery. Transgenderists may or may not seek hormonal treatment.
Transsexuals, on the other hand, seek to live as the gender 'opposite' to that of their birth, but unlike transgenderists they desire hormonal treatment and GRS to bring their minds and bodies into alignment.
Having these desires does not mean they can be attained. Health, financial and other issues may make it impossible for hormone treatment and surgery. A transsexual who cannot afford hormones and surgery is still a transsexual.
There is a lot of argument about whether a 'non-op' transsexual, someone who never desires surgery (not because of health or financial problems), should be considered a transsexual at all. When I read some of these arguments, I sensed a lot of politics behind them.
It seems to me there is too much emphasis on precise labels for people. Gender Identity can be fluid, for instance, and change over the course of one's life. My own experience leads me to believe it is more fluid for some than others.
Labels are important for justifying treatment to insurers. All of my estrogen is covered by my health insurance policy through my employer. A label of transsexual (or at least an interpretation of GID as meaning transsexual) is also important in those few situations where insurance covers GRS.
Last November, I spoke to a number of students at my undergraduate college. It's been several decades since I graduated.

. I was invited not so much because I am transsexual, but because I am also transgender. Transsexuality is simply one expression of a transgender identity. There were several students who identified as transgender and definitely not transsexual. I had a lot of fun speaking with them and hearing what their lives were like.