It also depends on the toys in the sanbox. If the GM does not like (just by way of example) weird fantasy magitech stuff, there is no possibility of the players engaging with that sort of thing in that particular game.I'll agree with that. I just don't particularly like the notion that sandbox is open to the PCs doing "whatever" because at there is always a certain point where things fall outside the scope of what the DM will allow. The walls of the box are somewhere. The difference is how much room the players have until they find them. A railroad has very tight walls. A linear adventure is a little wider. A sandbox depends on the size of the box, be it a region, a continent, a world or the Multiverse itself.
That is why I think it is worthwhile to remember that "sandbox" is a definition of playstyle, not a list of ingredients. it means "the players decide what to engage with, how and when" as a playstyle. That's all.