For me, "open world" and "sandbox" games are the exact opposite: An open world game typically has a semi-linear story "off rails" while a "sandbox" game is entirely free form much like kids playing in an actual Sandbox make their own fun.
To that end, games like The Elder Scrolls series are open world in the sense that you are free to explore, but there are specific objectives you're asked to complete in your own time. Sandbox games ask nothing of the player but often have clear progression systems they can follow or skip through at their leisure. Minecraft falls under this category because zero expectations are placed on the player, but you do have an order of steps that can be followed to unlock new activities.
That said, I agree with everything else in your post. Minecraft was a game that helped popularize sandbox games by pairing it with a survival element. As such, the survival and sandbox genres are often joined at the hip. Even though I've switched the definitions for open world and sandbox, I do agree that Breath of the Wild is an open world game because it had specific tasks you were asked to do but at your leisure.
I think a major component of the appeal for open world/sandbox games is the ability to "express" your interests in whatever manner you please. Open world games are free flowing and encourage players to essentially put themselves into the game by choosing how they engage with the content. Sandbox games often go a step farther by also providing players with the ability to create their own content. A great example of this is players using redstone in Minecraft to create calculators.
There are definitely times where game developers attempt to milk the "open world" and "sandbox" buzz words by providing a largely empty game world to explore. Sea of Thieves is a great example of this, as its initial release was largely lifeless due to predominantly empty islands littered all over the game world.
All that aside, I'm a huge fan of both genres when done right ;)
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I really agree with you on this. While linear games are highly enjoyable, the magic of being in a open world/Sandbox full of content and do as you please is something that many players around the world really like.
There's no wonder why GTA is a really loved franchise in the industry