Our notation isn’t clear about when a symbol stands
for a physical model in real detail, and when the
notation is a system of “meaningless signs.”
Suppose the analogy between “symbol with context” and
symbol stripped of context” is perfect.  Then the distinction
doesn’t matter.
People often assume that the analogy is perfect, and that the
distinction doesn’t matter.
But if we’re trying to check the transition between concrete
circumstance, and abstract math model, we do have to notice that
there is a distinction, and attend to that distinction.