Fawcett Comics is the comic book publisher that originally produced Captain Marvel comics. Captain Marvel was seen as a rip-off of Superman in the eyes of the publishers at DC Comics, and so a long lasting legal dispute ensued between the two companies. Eventually Fawcett stopped publishing Captain Marvel comics, and the legal dispute came to an end. However, eventually the company folded, and DC ended up acquiring the characters anyway.
Once DC Comics started publishing Captain Marvel stories, the comic book's name was changed to "Shazam!", which is the magic word Billy Batson says to transform into the well-known superhero. The word "Shazam" is the name of the wizard that gave Billy his powers. The reason for the name change was that Marvel Comics had the copyright to use the name.
During the DC years of comic books featuring the character of Captain Marvel, it was revealed that the Fawcett Comics universe was Earth-S. It was not part of the mainstream DC Universe, which was referred to as Earth-One. In other words, Captain Marvel and Superman were from two completely different earths, unaware of each others existence until they met during an inter-dimensional crossover adventure. Despite the fact that the JLA and the Marvel Family were from completely separate realities in the comic books, in the Superfriends universe, both the Fawcett characters and DC characters were all from the same earth, as seen in Legends of the Superheroes.
While in the comics, the Fawcett characters and the DC characters weren't part of the same reality until after Crisis On Infinite Earths, in which several earths within the multiverse were merged together, creating a single reality.
Although Fawcett Comics is long gone, the characters that came from that never-to-be-forgotten comic book company are still being published in comics from DC to this day.