Boy, that's a fun one to dig into. The biggest shift I notice is in pacing and focus. The official material has to keep a broad audience and push the sports narrative forward. Doujinshi can just... linger. I've read this one where Victor and Yuuri spend like twenty pages just grocery shopping in St. Petersburg, arguing about pickled plums and forgetting half the list. You'd never get that in the manga—it's all about the next competition. The fan works give them a mundane, domestic reality the show only hints at.
Then there's the sheer variety of tones. Sure, there's the fluffy stuff everyone expects, but I've stumbled onto some surprisingly melancholic takes exploring Victor's loneliness before Yuuri, or even darker AUs. The official story has a specific, uplifting emotional throughline. Fan creators aren't bound by that, so they can peel back layers the canon leaves untouched, or just go completely off the rails with mermaid AUs or whatever. It's less an extension and more a prism—splitting the source material into a spectrum of possibilities, some comforting, some challenging.