You're not getting it, clearly.
The term «quest» itself is a VERY loaded term, and such substitution is pretty much coming across as intentional obfuscation. It's not a commonly used term in the theory works I've read.
And, in practice, few people actually run real sandbox games on the TT. Many who claim to actually aren't doing so, because they have an agenda as a GM. If, at any point, the GM has to hint that, "The story is over here, guys" that's not a proper sandbox.
A large part of that is conflation with videogames, where quests are there in a supposedly open world that isn't actually an open world, but is instead quest-gated by need of certain items to get into specific regions.
The definitions of open world and sandbox differ significantly between the two media. Zelda games are said to be "open world" - but they are not. Large portions are locked behind needed items. That's a feature that few TT RPGs have, but many GM's try to impose.
When you get to the TTRPG, if an area requires having done X, Y or Z to have anything interesting happen, it's no longer a sandbox, it's just a wall-less dungeon.
I'm a 'bit' confused about what your definition of 'sandbox' is then...
A sandbox, to use the term in its purest meaning, is a setting in which some number of different 'engageable resources' exist, but in which the structure of the game doesn't apply ANY force whatsoever in terms of pushing the players to choose which ones to interact with. However, hints can be given, maps, information, rumors, etc. These are simply forms of intelligence which the party can gather, or which might fall into their hands over time in order to reveal the existing/location of these resources. This is the ideal of course. The players simply choose from the 'smorgasbord' of options, or perhaps simply blunder around the landscape hoping to fall into something.
However, there is no sense in which player agendas cannot or will not produce 'quests', they most certainly will! Players will evolve intentions, maybe as basic as "find the fabled Vorpal Sword of Snikersnak" and then go looking for it. Clearly this would arise after some sort of information is provided by the GM as to the possibility of success. The actual impetus however is coming from a player.
OTOH there are certainly sandboxes with meta-plot as well. They are simply 'time varying maps' in essence. However, because of the inevitable progression of the plot they will generate impetus which often doesn't originate in the players. These would be more like the 'side quests'
@Manbearcat is talking about. Often meta-plot is also set in motion, sort of like a 'landslide' by whatever the PCs did. They attack the orcs, the orcs declare war, the PCs must find the tomb of Sir Snikersnak if they are going to avoid getting the town destroyed (and its inhabitants are keen to see them hang for that). This is all likely fare in what originates as even the most pure sandbox.
The point is, there is often stuff the PCs cannot do, must do, should do, etc. even in a pure sandbox. While it is possible to simply ignore all such possibilities, I would call the result exactly what MBC terms "Rowboat World" a very shallow but extensive environment in which all that exists are some challenges to find and solve. Nothing ever changes, nothing progresses, there's no real 'meaning' to anything beyond its tactical significance, etc.