Homosexual transsexual (as opposed to autogynephilic transsexual). This is Ray Blanchard's transsexualism typology:

Michael Bailey, who supports this typology, describes it like this:

The two types of transsexuals who begin life as males are called homosexual and autogynephilic. Once understood, these names are appropriate. Succinctly put, homosexual male-to-female transsexuals are extremely feminine gay men, and autogynephilic transsexuals are men erotically obsessed with the image of themselves as women. When most people hear “transsexual” they think of the homosexual transsexual, who fits the classic pattern. From soon after birth, the homosexual male-to-female transsexual behaves and feels like a girl. [...] Honest and open autogynephilic transsexuals reveal a much different pattern. They were not especially feminine boys. The first overt manifestation of what led to their transsexualism was typically during early adolescence, when they secretly dressed in their mothers’ or sisters’ lingerie [...] Autogynephilic transsexuals might declare attraction to women or men, to both, or to neither. But their primary attraction is to the women that they would become [...] (The Man Who Would Be Queen, 2003, p. 146–147)

Many TRA's don't accept this. Alice Dreger, who studied the reception of Bailey's book, writes that this is because

there is the running theme started in the Preface [of Bailey's book] of the feminine essence narrative being a sometimes-willful lie told to cover up a sexual fetish, namely autogynephilia, and the associated theme that virtually all ‘‘non-homosexual transsexuals’’ are autogynephilic, no matter what they claim about themselves and their histories [...]" (p. 381)

So the division into HSTS and ATS implies that some transsexuals (namely, the ATS ones) have sexual or fetishistic motives, rather than every transwoman being a simple case of "a woman trapped in a man's body" (i.e. "the feminine essence narrative").

Dreger writes further:

I’m not sure that the simplistic feminine essence narrative is necessarily any better for transwomen than Blanchard’s typology. In doing research for this project, I have been disturbed to see the extent to which transwomen, in order to speak and be heard, seem to feel obliged to completely deny the role of eroticism in their decisions to undergo sex reassignment [...] Historically, this de-eroticization of transsexuals’ life narratives has been promoted not only by certain transwomen like Christine Jorgensen but also, importantly, by the medical professionals who have acted as gatekeepers to sex reassignment. After all, in the past, some influential clinicians claimed that confession of a single instance of sexual arousal associated with crossdressing should eliminate a patient from consideration of a diagnosis of transsexualism and thus also from consideration of sex reassignment [...] (p. 416)