Even in its current status where the Puyo Puyo games make up the majority of the franchise's output, I think the "Madou Monogatari" title has remained an appropriate descriptor. This really is, as Wikipedia's transliteration puts it, "a story of sorcery." Magic and the occult, particularly the craft of sorcery, are the main driving forces throughout the narratives of the franchise, even as the later ''Puyo'' games have mixed in characters and settings who do not subscribe to traditional fantasy. For example, ''Puyo Puyo 7'' mainly takes place in a world inspired by the real world, with characters including three middle school students and a cosmic entity serving as that game's antagonist. Other themes, such as parallel universes/dimensions (the ''Puyo Puyo Tetris'' games specify that Tetris exists in a different dimension from the Puyo-based universes), memories, and how feelings trascend interdimensional amnesia, are also observable. Utako Yoshino, a freelance writer who has written for ''Puyo Puyo'' games and other media, has expressed that they are very difficult to work with in terms of showing continuity and character growth in the games, but you can make some of that out if you look for it. If SEGA is strict in senses such as that, then Compile was pretty much the opposite. A bio for original protagonist Arle Nadja more or less said that "her backstory is different depending on the game". They were pretty open about that they were not very concerned with consistency in the Madou world or storyline. Most people accepted this, but one writer at Compile was allowed to officially publish his interpretation of the franchise, attempting to weave the ''Madou'' and ''Puyo'' games together into one timeline. This was known as the...

Kenji Oda was a writer at Compile, who had a few high creative roles in Madou/Puyo games, but perhaps most notably worked on the "True Madou Mongatari" light novel series. Included in the first volume of this series was the first edition of the Madou Monogatari Chronology, which is the only timeline that has ever publicly been released for the franchise. A lot of it is simply placing the existing games about where we already knew they would go, like that any version of Madou Monogatari 1 would be 10 years before Madou Monogatari 2. However, a lot of the timeline is backstory to the universe which was not shown in any media, taking the Judeo-Christian themes and concepts already present in the franchise much farther. In Oda's timeline, it is established that main antagonist Satan, as in the Bible, is a fallen angel who used to be named Lucifer. He was in love with a woman named Lilith, a powerful mage who seemed to have lead humanity in the war against the heavens. As a last resort, Lilith used an artifact called the Seraphim Orb to create the World of Sorcery, the homeworld of most characters established at this point. It is in Oda's writing, however, where characters were first established as able to come from universes besides that of Atle. Ragnus Bisashi, who in the ''Puyo Puyo'' series was mostly used to joke about Dragon Quest, is played straight in the True Madou series and Sega Saturn game, where he is shown to come from darker fantasy realm known as Gaiearth. This is honestly a move that I respect a lot, and one that I believe is considered canon by SEGA when he is described as "an otherworldly hero." From my observation of the fanbase, Kenji Oda's vision for the franchise is no longer taken as canon at face value, but certain aspects have still made their way into SEGA's Puyo games and are part of some fans' headcanons for the setting and characters. In a nutshell, the canon for the games under Compile is very loose and ultimately doesn't matter much, but the SEGA games (beginning with ''Puyo Puyo Fever'') paint a clearer picture for story stuff, and their canon timeline from that point on is about the same as the release order. But as for me, I really admire Oda's attempt to bring the franchise's universe at that point out of the status quo of its first game, with its many holes, even if his writing starts to lose people around explaining the ''Madou-Puyo'' split with a reset of that universe. But the hints that it still matters at least a little in SEGA's run are there.