Sandbox is just another name for open-world, basically.

It's really not. Sure, you'll find plenty of articles to that effect all over the internet, but we're better served looking at them as separate concepts.

They are so easily described as aspects that aren't at all mutually-inclusive that I don't know why anyone still considers them synonymous.

You can absolutely have sandboxes that aren't open-world (Dishonored, Portal), those that are both (BOTW), and then open-world games that aren't sandbox (Skyrim, TW3), and then a bunch of in-betweens:

MGSV is more sandbox than OW, but has plenty of OW elements. Fallout and GTA are more OW than sandbox but have a lot of sandboxy stuff you can do.

Open-World is more about character and story progression options, map-traversal, mission order and interaction, and their activation/start/opt-in.

Sandbox is more about the gameplay itself - especially physics and tool-sets (and how those tools work). And often, these things are built somewhat separately from the world's look. They aren't tacked on to work within, they dictate how the character interacts with the world.

Often times sandboxes are designed such that the developers themselves aren't sure what's all reasonably possible (barring bugs and glitches, that is).