[5] Thus, to extend this conjecturally toward our original question: when someone asks "Is the physical world 'real'?" they may, in part, be asking whether their predictive models of the physical world will give accurate predictions in a very robust manner, or whether they are merely local approximations. The latter would hold if e.g. the person: is a brain in a vat; is dreaming; or is being simulated and can potentially be affected by entities outside the simulation.

Hmm. Let's say we live in a multiverse where there are infinitely many universes with laws we cannot compute, so our laws are very much local (but not necessarily approximations). Would it make the world as we know it less real? I would not feel that.

On the other hand living in a simulation would feel unreal, though it might be based on a fantasy that you can 'break out' somehow.

Another use of the term is authenticity; e.g. I'd be proud to own a book signed by Churchill, but ashamed if it was a fake. (Physical laws to not dictate either way - it could have been authentic). This last example makes me think that it's going to be hard to disentangle the term from its psychological connotations.