> Conjunction and disjunction are more apt anologies that have the same properties.

Conjunction and disjunction also have other properties, like idempotence: A /\ A = A, which by analogy would suggest that a tuple of two integers is the same as a single integer. Similarly, A \/ A = A, which is exactly the problem mentioned by the featured article that is the difference between union types and proper sum types (aka tagged union types).

So while sum and product may not be great analogies, conjunction and disjunction seem worse.