FWIW, the distinction we're considering in this thread is related to the notion of materializability of collections I pitched in this thread: Introduce a `MaterializableCollection` protocol. With that in mind, another option would be MaterializableSet: SetAlgebra, Collection.
This name makes some sense: a user of these sets isn't really concerned with how they are defined (that's an implementation detail). Instead they are concerned with what they can do with the set. The capability introduced by the proposed distinction is precisely the ability to materialize the elements of the set rather than simply check for membership.
Aside from naming, I think there are additional details that need to be considered while we're reforming SetAlgebra. I would expect to see these covered in detail in a draft proposal. For example, Equatable and ExpressibleByArrayLiteral refinement should probably not live on the base SetAlgebra protocol. PredicateSet cannot conform to Equatable. In theory it could conform to ExpressibleByArrayLiteral, but should it? This requirement may be more problematic for other kinds of intensional sets.