It is the same thing! I am totally fine with that name, it is the full official title.

The original anime, it’s movies and most the manga are the same universe. In exchange practice everyone is combined in the tag for the Madoka Magica anime. Magia Record is it’s own parallel Earth with its own version of the anime characters, all the manga characters I listed, plus it’s own original characters. The only character that I know of who is explicitly the same character is the game Ultimate Madoka is the anime universe’s Madoka, not the Madoka native to the game universe.

As a note, the English version is a few chapters behind the Japanese version.