I hope the Players Handbook is the ONLY core book.
This Players Hanbook is like the 0e Rules Cyclopedia, the 4e Rules Compendium, the 3e SRD and Pathfinder Rulebook, and so on. This book has all the rules for both the DM and the heroes, and is the only book that players need to buy to play a game of D&D. It includes combat rules for terrains, such as aquatic and flying. It has all the rules for a complete game. But then the DM uses the races for the hostiles in combat encounters.
All other books are supplimental.
The Dungeon Masters Guide goes into depth about designing adventures (compare 4e DMG 1 and 2) and gives all the ‘advanced’ game-changing mechanics (compare 1e Unearthed Arcana), including tactical grid wargame style.
The Setting Guides are more important in 5e than in previous editions. Because 5e is highly modular, each Setting Guide sellects the specific options for a particular playstyle, genre, and mood. Setting Guides include Planescape, Forgotten Realms, Nerath, Eberron, Dark Sun, Dragonlance, hopefully Modern Urban Arcana (but with normal D&D classes), Ravenloft, and so on.
Setting Guides subdivide into ‘World Settings’ and ‘Regional Settings’. The World Setting defines the Setting as a brand name, and focuses on the cosmology, religions, and overall premise of the Setting. The Regional Settings are specific locations that can easily plug-and-play into any Setting. For example, one can easily plug the subterranean Drow city Menzoberranzan, which is one of the Forgotten Realms Regional Settings, into the Dark Sun World Setting. Oppositely, a Dark Sun city could plug into the Forgotten Realms World Setting as a location in a desert region, or even in the Plane of Fire.
The Monster Manual is a bestiary that adds new kinds of monsters that the DM can use as exotic hostiles. Possibly the Monster Manual needs to divide up by setting. So, ‘Monster Manual of Planescape’, ‘Monster Manual of Eberron’, ‘Monster Manual of Nerath’, ‘Monster Manual of Forgotten Realms’, ‘Monster Manual of Ravenloft’, and so on. Even if the Monster Manuals divide by settings, the entries need to be designed for straightforward plug-and-play into any setting.