Labels are sometimes necessary depending on the circumstances and the context in which the subject of one's sex/gender arise. For example, I recently found a new primary care physician to look after my health needs. In my introduction, I informed her that I was a post-op transsexual woman. That description was meaningful to her. Describing myself as 'transgender' would have been ambiguous, requiring further explanation. If I had simply identified as a 'woman', I would have been withholding pertinent information important to future medical advice and treatment with potential consequences to my health and well-being.
I will refer to myself as transgender when the details of my situation are not really germane to the conversation. The way I see it, sex and gender are two separate characteristics of a person. One's sex is a physical characteristic, while gender is a social/behavioral characteristic. I am transgender because I once identified as a boy/man, but now as a woman. That is, I went from identifying and presenting as a man to identifying and presenting as a woman, first part-time, and, eventually, full-time. My sex remained male during that time. I might have further identified as a drag artist, cross-dresser, transgenderist, or described myself as gender fluid, non-binary, or gender queer. No matter the label, physically I was still male.
But despite having changed my gender identity from male to female (as others perceived me), I was still physically male which was very discomforting to me. I had strong male body dysphoria. The expression 'trapped in a male body' felt very real to me. I needed to go beyond changing my social gender identity to transforming my bodily sex from male to female. That need/objective distinguished me from transgender people who have no need or desire to medically alter their bodies. I began the long process of transforming my physical sex from male to female.
Like Charley, I identity simply as a woman. A female woman. No other qualifier is necessary under ordinary circumstances. But if my past must be divulged, transsexual is a more precise descriptor than transgender.