Confusingly, there are two different things called disjoint union in mathematics. One is what you mentioned, which is indeed the coproduct in the category of sets. But another one is simply the union of two disjoint sets, which might not be too common in programming, but is used quite a lot, say, in analysis and point-set topology. Flow's use of the term obviously refers to the latter.
The former is a (small) generalization of the latter, tacking on a tag to forcibly ensure the sets are disjoint. It's not worth thinking of them as different.
In any case, Flow doesn't require that the sides of the | are different.
(The Flow use of the name doesn't seem to quite match the mathematical definition.)