A tiny but vocal minority of cisgender LGB people argue that trans issues are distracting from "original" gay rights. This movement is widely condemned by mainstream LGBTQ organizations, but it exists, highlighting the fragility of the alliance.
The term "transsexual" (often used in the 20th century) focused on medical transition. The modern term "transgender" focuses on identity. This shift was driven by trans activists within the LGBTQ umbrella.