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.
Sure was. The iZombie comic provided the basis for the TV adaptation. The comic had its own unique storylines and characters that were carried over in some form to the screen.