I'm perhaps way off, but to me sci-fi is pretty much any narrative that mirrors our own world but with specific differences that have an effect on the story. Eg a story that's a regular setting but everyone has to pay for oxygen, or a story set in an alternate history where the British empire never faded. The differences are variables that can be used to view humanity from a different perspective.

To me Star Trek and Dune are essentially fantasy settings. Star Trek though obviously has sci-fi stories. Eg depicting a broadly post-racial society but using aliens as a tool to explore racism in our own culture.