I'd suggest not using ENWorld as the place to try to define things. We can't even agree on what an RPG is, so trying to define things like railroading, linear adventure, or sandbox are going to be harder still.
I mostly run open-world sandboxes. It's something like a mix of your moderate, advanced, and ultimate sandbox definitions. But not exactly.
Pre-made or homebrew world. Work up some notes on the starting town which includes NPCs, factions, situations-hooks, etc. Create a few nearby points of interest to explore and interact with, along with whatever NPCs, factions, situations-hooks, etc those require. Make sure they point to other points of interest or back to the town. Discrete points on an ever-expanding web, basically.
Check in with the players to find out what some of their goals or their PCs' goals are and incorporate them into the setting if they're more quick and immediate or start thinking of how to fit them in later if they're more long-term goals.
Giving the NPCs and factions goals and timers is also important. The PCs don't exist in a static world. I don't need to know what the PCs will do, only what the NPCs will do. Unless the PCs stop them, the snake cult is going to kidnap the prince in one month...and unless the PCs stop them, the snake cult is going to sacrifice the prince one month later. I know the king is going to be pissed if the adventurers fail and even more pissed if the PCs accept the job then abandon it. There is no pre-defined story. Only NPCs and factions with goals and interesting locations. Everything changes when the PCs get involved.
Drop the PCs in the starter town and let them go. Play is usually the PCs bouncing off NPCs and factions, picking up jobs or abandoning them, following their own goals or abandoning them, but all the while they're making an impression on the NPCs, factions, and setting. Action and reaction are key to making a sandbox feel like a living, breathing place. Consequences for actions or inaction. Rewarded for saving the dragon from the princess or hunted by the kingdom for abandoning the prince to the snake cult. Create a drama-tension rich environment and wind it up before dropping the PCs in and seeing what happens. You could rewind back to 1 and use all the same material for a different group and it would play out completely differently every time.
And of course the improv, always so much improv.
I have a stack of modules to drop in if I need them, a stack of random encounter tables if I need them, and the old pulp trope of send in a goon with a sword if I need to stall for time. If all else fails, I can simply put an obstacle between them and their current goal.
The difference between a sandbox and a railroad is night and day. The players have real choices in a sandbox whereas they don't in a railroad. At a guess this is a spectrum and whatever linear adventures are they are either somewhere between the two on that spectrum or orthogonal to that spectrum.
If you're looking for sandbox resources,
there's a thread for that. Link to my post there. There's lots of great stuff out there for sandbox play.