Therefore if we assign to one of the possible worlds the status of "actual world" by realist principles, (which would constitute a modal difference), we would be attributing a difference to this world which violates the modal system which dictates "no modal difference". — Metaphysician Undercover

I don't know what realist principles are. The thing is, there is a system of modal logic which, I understand works reasonably well by the relevant standards. I've no desire to interfere in something I don't understand. So, if the logic says there is no modal difference, I shall treat that in the same way that I treat the logical operators of implication, conjunction and disjunction - as technical concepts which do not need to mirror ordinary language. That mutual tolerance seems to work quite well.
However, it seems that it is not a question of two worlds, with a difference between them, but a difference of the same world. If the difference involved here is not a difference in the description of the possible world, it must be a difference in status of that same world. (Compare Kant's argument that existence is not a predicate, because to assert that X exists is not to identify that there is any difference between X as conceived (or even possible) and X as existent (or actual).

The alternative, non-Platonic realism would say that we create, produce or "construct" knowledge while something other than knowledge is what is independent from us. There are also forms of realism which blur the boundary between these two by invoking concepts like "information". — Metaphysician Undercover

I don't think that any of the critical terms in this debate are at all well defined and there's a wide range of choice available. It can make it very difficult to know just what label applies to oneself.

So we can avoid "annoying debates about what is a thing and what is not", and move along with our mundane communications without the need to address metaphysical differences. If however, metaphysics is the subject of discussion, then avoiding these annoying discussions is a mistake conducive to misunderstanding. — Metaphysician Undercover

H'm. Maybe. I agree, however, that more would need to be said about what "discover" means. But I like the implication that discovery presupposes an independent pre-existing something. It's not difficult with the empirical, but the a priori needs careful handling.

The thing is, there is a system of modal logic which, I understand works reasonably well by the relevant standards. — Ludwig V

I agree.

However, it seems that it is not a question of two worlds, with a difference between them, but a difference in the same world. If the difference involved here is not a difference in the description of the possible world, it must be a difference in status of that same world. — Ludwig V

Ok, let's consider this perspective then. The representations of modal logic, are different possible descriptions of an independent actual world. It should be clear to you that none of the possibilities is the actual, independent world. Therefore it should also be clear to you that none of the possibilities is the actual. To think such would be a case of what is commonly called confusing the map with the terrain. We can establish some principles for judgement, criteria of truth or whatever, but that produces a judgement of truth, it does not make one of the possibilities into the actual.

H'm. Maybe. I agree, however, that more would need to be said about what "discover" means. But I like the implication that discovery presupposes an independent pre-existing something. It's not difficult with the empirical, but the a priori needs careful handling. — Ludwig V

Well, the issue is what exactly is the nature of what is termed here as "an independent pre-existing something". If we talk about discovering knowledge, then we imply that the independent something which we discover is knowledge. If we talk about discovering true statements, then it is implied that the independent something discovered is statements. If we talk about discovering information than it is implied that the independent something is information.

Conventionally, we would assign "matter" to the independent something. But Aristotle demonstrated that matter on its own is completely unintelligible, therefore unknowable. It is actually the form which the matter is in which is intelligible. But this poses the question of what exactly is "form", and how does it make something unknowable, matter, into something knowable.