"If time appears discrete (or continuous) at some level, it could still be continuous (or discrete) at higher resolution"
This seems to imply that a measurement of a discrete space-time at some resolution does not imply "fundamental" discreteness
This is correct - there can be detail which is continuous but which you have not the ability to resolve and hence only see an apparently discrete change.
and hence discrete and continuous space-times are equivalent descriptions.
This is not necessarily the case.
We don't really know the consequences of such discrete space-time, but we would presumably reach a point at which resolving differences between discrete and continuous is possible. Put crudely, you'll notice an edge.
However we would expect a discrete space-time to have a limiting case (when considered at a large enough scale) to match our continuous models, simply because we know those models work well at the appropriate scales.
So I would like to know:
How can a continuous (space-) time look discrete on a LARGER scale?
The argument is fairly simple. Imagine on a very detailed scale (a small scale) a graph has a level region which then develops a very steep (but continuous) slope to a new level.
Now "zoom out". Zooming out the steep slope stops looking like a slope and starts appearing like a vertical line. You cannot, with measuring tool scaled to that level of "zoomed out" detail, resolve the co0ntinuous slope from one level to another and it appears simply as a sudden change from one discrete level to another - a step.
So at a larger scale it can seem discontinuous, but on a more detailed, smaller scale, it can appear continuous.