If the same bridge-law structure does the work in both cases, the distinction in the nature of the relata collapses into a merely notational difference rather than a genuine categorical one.

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Notational difference(in philosophy of science and logic): A difference that only exists in how you write or describe something, not in what the thing actually is.
Relata(in philosophy of relations): The individual things that a relation connects—for example, in 'Alice loves Bob,' Alice and Bob are the relata (the things being related).
bridge-law(as used in philosophy of mind and metaphysics): A rule that connects or translates between two different types of descriptions or systems—like a bridge that lets you move between two sides. In this case, it's a way of showing how two different things relate to each other using the same underlying structure.
categorical(axiomatic theories in logic): A set of sentences is categorical if and only if all of its models are isomorphic, meaning there is only one model up to isomorphism.

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