Afaik, the renaming was part of the WG's attempt at downplaying the fruit, since if they can't have it, at least they can make it seem like a pointless power to seek.
Both Katakuri and Doflamingo awakened paramecia-type devil fruits. The main commonality is the ability to manipulate the surrounding environment into a material resembling their powers. Kinda like how Luffy can turn the rocky terrain into rubber, they were turning theirs into mochi and string. The plot twist of Luffy's fruit being a human-human ancient deity type fruit, however, makes his more comparable to Sengoku's Buddha fruit.
Also, for DarthEnderX:
https://www.reddit.com/r/OnePiece/co..._pacing_audio/
An actually well-edited fix of the episode.