No, they're not exactly the same. DC Comics is the original source of the characters and stories, while the DC Universe is a broader platform that includes various media adaptations and related content.
In DC Comics, 'DC' stands for Detective Comics. It was originally the name of a comic book series that later became the basis for the entire DC universe.
DC Shoes and DC Comics have no direct connection. DC Comics is famous for superhero stories, while DC Shoes focuses on producing shoes and related apparel. There's no ownership or business link between them.
Thor doesn't kill Zeus in the comics. The storylines usually focus on their conflicts and interactions without going to the extreme of one killing the other. It's part of the complex web of comic book narratives.