Dividing spells up into Arcane, Divine, and Primal got left behind in early playtests. The 2024 PHB uses class-based spell lists similar to how 2014 PHB treats things.
In general there is still some thematic impact of the Arcane, Divine, and Primal lists, like how Magical Secrets for Bards or Magic Initiate feats can only select from the Cleric, Druid, or Wizard spell lists (being the archetypes of Divine, Primal, and Arcane spells, respectively). But there is no official definition of these three spell types anywhere in the book.