Which game engines have been used by FromSoftware for what and when is an age-old question shrouded in mystery and misinformation. This page will attempt to clarify the matter, while still providing no information of any actual practical use whatsoever. The various engines From uses are described below, in vaguely decreasing order of relevance.
Dantelion
"Dantelion" is the modding community's name for the modern From engine, first created for the launch of the PS3/X360 generation and continuing to evolve to this day. There is no known official name for the engine; maybe they simply call it The Engine, maybe they refer to each iteration of it by the project name at the time, or maybe they dare not speak its name for fear of invoking its ancient wrath. Whatever the case may be, we need something to call it, and although many aspects of it have changed over the years, at least one thing remains constant: dantelion2, a low-level core component of the engine which seems to be responsible for memory mapping, cross-platform utilities, debugging, etc. It has been present in every game from Enchanted Arms onwards, it sounds kind of cool, and we don't have anything better to use, so here we are.
Dantelion is an entirely proprietary engine developed by and for FromSoftware; although it typically makes use of common middleware such as Havok, Fmod, or Bink, the vast majority of its systems and formats are custom-made, undocumented, and unsupported in any existing software. Given that, almost all modding tools used for From games are the product of reverse-engineering and implementation from scratch by the community. Especially more recently now that their presence on PC is stronger and modding has become more prevalent, From tries to avoid shipping any unnecessary information that would be helpful, and although they don't try very hard to prevent modding, they clearly don't approve of it either.
Whether Dantelion should really be considered simply "an engine", a series of engines, or a family of them is unclear; Demon's Souls, Dark Souls, Bloodborne, Dark Souls 3, and Sekiro have an extremely clear lineage, but some older games seem more distant, and where one draws the line is most likely a matter of taste. Enchanted Arms, for example, appears very similar to Demon's Souls and its ilk, whereas the Armored Core games, as you might expect, are structured quite differently, despite still sharing the majority of their formats and components. However, since many older games have not been studied as thoroughly, they can all broadly be considered to be "the same engine" in the absence of any clear distinction. Overall, Dantelion is like an ogre: it has layers. Each game builds upon the last, adding some things, replacing others, and (rarely) removing them. For further consideration, please refer to the Ship of Theseus.
An amusing historical note is that the first "game" published on the Dantelion engine was actually HD VISUAL Preview Disc, a promotional disc for the PS3 which allowed you to view two trailers for Enchanted Arms and Armored Core 4, and which is secretly just the game engine being repurposed as an ad hoc media player. This legacy was finally revisited in recent years with the release of Sekiro's digital artbook and mini soundtrack on Steam, which is, again, just Dantelion in a trenchcoat. In all likelihood, the Elden Ring "Deluxe Edition" will tell a similar story, although that has yet to be confirmed.
Katana
"Katana" is the name given by the community to the engine used in Dark Souls 2 specifically. This name is even more tenuous than "Dantelion", only being referenced by a few random strings in the executable, but again, we have to call it something. As for why DS2 is considered its own engine when even games as far afield as Another Century's Episode: R aren't, that is a matter of much debate. Although DS2 shares a fairly large majority of its file formats with its successors and predecessors, the engine itself seems to have been significantly modified, or even rewritten. It exhibits fundamentally different behavior around saving, character control, scripting, map layouts, and more.
DS2 does still include ol' reliable dantelion2, so a case could be made for it counting as another "Dantelion" game, especially since it does at least have a very clear relation to them, if not an exact lineage. In some ways it even seems to be more of a descendent of the branch of the engine used for various mech games, or perhaps an ungodly merging of that with the "main" action RPG branch, plus plenty of unique and bizarre quirks all its own. In any case, whether it counts as a Dantelion game or not, it is distinct enough to warrant its own suitably edgy designation: Katana.
Unreal
Unreal Engine has so far only been used for Déraciné, presumably to avoid having to implement VR capabilities in Dantelion. There is a very small amount of overlap in the form of some file formats being shared, but for the most part it bears no relation to the other games or engines.
Phyre
Due to a combination of vagueness, repetition, and stubborn wiki editors, the Souls series was for many years widely believed to run on Sony's Phyre engine. Once the games were actually examined internally it became abundantly clear that this was never the case, but in an amusing twist of fate it transpired that Metal Wolf Chaos XD, which was not developed by From, does actually use Phyre. To our knowledge this is the only From-adjacent game that has any connection to Phyre whatsoever.
Other
This page conspicuously excludes any games before the PS3 era, for the simple reason that I do not know much about them. A natural question is whatever happened to dantelion1 if Enchanted Arms started right off with dantelion2, but so far no evidence has surfaced that it was used before then. Whether that's to do with the name simply not being baked into the executable before then or due to it being something else entirely is as of yet unknown. There are a small handful of file formats which can be seen in a more primitive form in certain earlier games, but even those were changed significantly for the modern engine and very little else seems to have survived the transition.
Finally, the PSP, DS, and 3DS games which were released after the creation of Dantelion deserve mentioning, if only to say that they appear to be entirely separate from it.