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.
DC Comics has indeed been bought. The acquisitions are part of the dynamic landscape of the entertainment industry, where companies seek to consolidate and grow their presence in the comic book and related media markets.