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To begin with, the old gay-rights movement did not win the effusive backing of Tories, cops, CofE bigwigs and the entire educational establishment, as the trans movement has.
Stiff Tories were not falling over themselves to institute laws that would heap 'recognition' on gay people, as they are today with trans people: see the Gender Recognition Act, an eccentric, reality-defying proposed tweak to the law that would allow anyone to change sex as casually as they change their hairstyle, which is being championed by Theresa May of all people.
Also, the old gay-rights movement agitated against the idea that their sexuality was a mental disorder, as it was horribly defined by American psychologists up to 1972. In contrast, the trans-rights movement craves medical diagnosis, in particular of the mental malaise 'gender dysphoria'.
Warriors for gay rights demanded autonomy, from medical paternalism, state policing and moral-majority approval; the trans movement seeks these things. It wants validation rather than freedom. State backing rather than state absence. And the approval of every social and cultural institution instead of not giving a fig what these people think.
Comment: See also: