The "Dark Knight" job is weird.
In Final Fantasy, the Dark Knight job is usually consistantly referred to in the Japanese games as 暗黒騎士 for "Ankoku Kishi". Looking at III's Dark Knight job, however, this isn't the case. Instead, it's referred to as "魔剣士" or "Makenshi".
Makenshi is a different term in Japanese, usually meaning either "Magic Swordsman" or "Cursed/Demon Swordsman", although Final Fantasy V's Mystic Knight or "Magic Fencer" uses the strikingly similar term: 魔法剣士.
When the remake came around, the job was translated simply as "Dark Knight" matching the other depictions in the series. Despite (and the new skill even encouraging this) the job retains its "Cursed/Demon Swordsman" name in Japan. To make things weirder, the job was going tp get a new name in the remake, but it was going to be called "暗黒剣士" or "Darkness Swordsman" as that is the name used when the job comes up in the unused text. Final Fantasy: The 4 Heroes of Light would eventually use the term, with the resulting translation being "Dark Fencer".
But it gets even weirder. Final Fantasy Brave Exvius has a character named Duane who is a nod to the FFIII job. In a tweet introducing him, he is identified as a "dark knight" but his infograph identifies his job as "Warmage". And then later, a variant of Luneth with the job is released, identified as... "Dark Knight Luneth".
Lastly, Bravely Default 2 featured a reimagined version of the job as one of numerous references and callbacks the game has to the series. This variation kept the "Demon Swordsman" elements and mixed them with Spellblade techniques, making it a fulfillment of both potential readings of the name. When BD2 was localized, this job was given a completely new name known as the Hellblade, despite it using the same terminiology as III's job in the JP version.
So... What differentiates a Dark Knight from a Warmage?
The original Famicom III gave Dark Knight white magic, but the remake gave it the Darkness ability. This is not unfounded, as Final Fantasy Tactics' take on Falgabard notes that the Dark Knights who inhabited the village had their lives cut short by their dark blades. Later games have followed this connection: Duane from Brave Exvius snapped due to intense stress combining with his exposure to the darkness, in a way akin to how lesser Dark Knights fared in FFIV's lore. Final Fantasy Dimensions uses the traditional term for Dark Knight and models it closely after Cecils', but uses Falgabard as the region where they hail from (albeit as a kingdom complete with castle rather than a village). The War of the Lions version of Dark Knight seems to take heavy cues from the Warmage despite it being said that they were primarily inspired by Cecil Harvey.