Basic question

Is there a definition as to what constitutes an "isolated" vs.
"non-isolated" circuit? What does this really mean? This is what I
think the definition really is:

A system S1 has an input V1,In referenced to V2,In and an output V1,out
referenced to V2,out whereas V1,In - V2,In has an operating limit of L1
and V1,out - V2,out has an operating limit of L2.

Is an isolated system a system that can have the references V2,In and
V2,out such that |V2,In - V2,out| >> 0 and still operate properly? If
so what value of |V2,In - V2,out| constitutes an "isolated system"?

Does anyone know of a formal definition of an "isolated" system? I
know that usually it's some kind of LED operating on some kind of
photo-sensitive device, but is that what the definition is limited to?
I don't think so because a "relay" is usually called an isolated
circuit.