CBS knew that that Addams family, already established through cartoons, was readily primed for a TV adaptation, and decided to create a property out of it without the rights to its characters.
When ABC found out this was going to happen, they readily greenlit a series for the actual Addams family to finally be translated onto the screen. If it weren't for CBS' eagerness to make the show, the Addams family itself may never have been made.
The Addams family was well established, and as it's script was written by Nat Perrin (Who wrote for the Marx Brothers) CBS understood what tone the show would be in, and tried to replicate it.
Despite the Addams family being the progenitor, the Munsters actually received better ratings.