Well, according to
F95's official definitions for tags, a sandbox is "free-roam types of games". IDK that I personally would call it a sandbox myself, either, but the game is tagged (perhaps incorrectly) as such. Sandbox is
supposed to be what you've described. But I generally try (and fail sometimes) to avoid quibbling about tag applicability, especially because it's often a matter of semantics.
Some people take the nature of sandbox to the extreme, for instance. They'll claim it's sandbox if you ever, even once, have to click room navigation to view an event or anything. That's not really the spirit of sandbox, which is more about visiting locations individually to find something to do. In games similar to VNs /KNs in style, that generally equates to having an event with someone to either advance the plot or increase stats with a LI. In more grindy games, that will also include things to improve the MC's stats (strength, charm, etc.) or to do a search for some item or a clue.