There isn't an Old West section here, so there's not much to take into account there. If horror is a consistent or ubiquitous theme it may be easier to just toss it in the horror section.
Here's some philosophical commonalities/redefinitions that apply to Science Fiction and Fantasy that may help you.
Fantasy is about creating a fantasy, invoking a mood and a place and a presence. by that I mean it's supposed to entice the reader to explore a new world. Not because it makes sense, but because it's full of interesting things. Therefore people are expected to take the existence of certain things for granted. DOOM, in this sense is more science-fantasy than science-fiction. It doesn't explain how humans are really able to get to Mars and then open up a portal to Hell, or where Hell is in the physical plane of time and space, it invites you to explore a world with demons and shotguns because demons and shotguns are interesting. Star Wars is a fantasy story in sci-fi clothing. They're space wizards with crystal swords in a universe inhabited by giant worms and a slug mafia. Protagonists tend to be (but are by NO MEANS limitted to) heroes or villains or other people actively involved in the world and doing things, since that is a good way to provide the reader with lots of little threads and subtleties about this new and mysterious world the story takes place in as well as with the general strokes provided with the rest of the story.
Science Fiction is about invoking wonder and thought in the world. In Sci-Fi, the reader is led to believe that this story is taking place in the real world, or that it could happen in the real world. Sci-Fi will talk about the implications of things like political/philosophical extremes, scientific theories and other things. Science Fiction is meant to speculate and invite speculation. Protagonists, rather than heroes and interlopers actively interacting with and exposing the world, usually (again, not at all always) do a lot more exploration and observation than actively taking part. Hell, the whole alien-non-interference clause that a lot of stories have enforces this principle. Science fiction on a more fundamental level is about invoking thoughts like, "Wouldn't it be cool/scary/dangerous/comforting to have knowledge/technology/encounters/societies like this in the real world?" rather than "I want to know more about the place this story is set in."
There's a lot of mixing and matching to be done here, and a lot of stories mesh pretty plentifully into both genres. Fallout explores technological and philosophical themes in the real world while taking place in a timeline very, very different from our own and attributing almost magical properties to the abilities of Science and radiation. Likewise, a lot of Lovecraft's settings ask us to take magic, monsters, and technology for granted while also inviting us to contemplate the very real-world horrors of existential indifference and insignificance in the face of immeasurably greater things. If you want to be in Everything Else only as a last resort, it's pretty easy to switch out most of the EE stories that are actually narratives rather than games into either of those catergories based on what they try to evoke.