Star Wars is accepted as Sci Fi in popular culture even though technically it isn't. I consider it a Fantasy. But i think you were right in calling it a Space Western. Actually i think the correct term for it is Space Opera. Star Trek was a Space Western too - "Band Wagon to the Stars"?
Define Sci Fi? Easy. Science fiction is a genre of fiction dealing with the impact of imagined innovations in science or technology, often in a futuristic setting.
P.S. SF actually means Speculative Future and is not Science Fiction. SF is the same as Sci Fi but minus the science.
Potato, potato. It's nigh impossible to define SF, SciFi, science fiction, Science Fiction, Scientifiction, speculative fiction, speculative future (that's a new one for me btw =), scientific romance, voyages extraordinaires etc etc, although it usually is easy to look at a specific title and say whether or not it is SF.
With your definition works from the new wave of the sixties like Dune or The Left Hand of Darkness or even Hyperion of recent years could be argued not to be part (since the estrangement in these novels for the most part isn't really based on science) of the same genre as The War of the Worlds (although it could be said that WotW can't be SF since the genre SF didn't even exist in the 1800s) or The Forever War.
I'm quite partial to Darko Suvin's definition: 'SF is, then, a literary genre whose necessary and sufficient conditions are the presence and interaction of estrangement and cognition, and whose main formal device is an imaginative framework alternative to the author's empirical environment.' In my opinion this estranging device, or novum as Suvin also refers to it, doesn't necessarily have to be a technological or 'hard' scientific object or event. It can as well be sociological novum.
If you ask 5 different literary critics to define the genre you'll end up with 5 different answers. In the end Damon Knight probably phrased it best with the oft quoted definition 'science fiction means what we point to when we say it.'
