Alien is Sci-Fi/Horror. Terminator 1 is Sci-Fi/Action with some horror elements.
Horror and sci-fi are not mutually exclusive categories. Alien is my favourite horror film though.
Sci-Fi as well as fantasy to some extent isn't really a genre so much as a setting, Alien is horror in a pretty solid sci-fi setting while Terminator 1 is a horror/thriller with light sci-fi elements.
A pretty common explanation of science fiction is speculation about how technology and culture effect our lives. a lot sci-fi is set in the future, but is about contemporary events. Alien is about corporate greed and corporate violence and working class life. Terminator is about nuclear war and cops and losing your humanity. Like Terminator uses a speculative robot from the future sent back by a speculative out of control nuclear war AI to muse abut the seemingly inevitablilty of a global nuclear war; It's so inevitable that even after it happens an AI will use time-travel to ensure it must happen. Stuff like that.
