I think broad genres are ok and perhaps useful, but overly specific ones only lead to limitations and imitations.
But to answer your questions, here's how I see them:
I see "Science Fiction" as what people often refer to as "Hard Science Fiction." The story has to have some type of science or technology that doesn't currently exist but is plausible, consistent and central to the story.
SF and Sci-fi are stories that have technology that doesn't exist and is never likely to exist. In most cases, you could tell the same story in a different setting by changing the setting and replacing all the implausible tech with equally implausible magic, but you cannot tell the story without removing the elements.
Fantasy is any story that has some element that magic or an unreal element that is central to the story.
Horror is any story that is trying to scare or horrify the reader.
Even with definitions this broad, it's sometimes hard to determine which genre a story belongs in. For example, is the movie Alien a horror movie, a science fiction movie or a SF movie?
Having said all that, I don't have a favorite genre. A good story, regardless of genre, has strong characters, a good plot, tension and makes a connection with the reader.