How can I disambiguate a type and a module with the same name?

The type can be disambiguated using the little-known import (class|struct|func|protocol|enum) Module.Symbol syntax.

import struct BTree.OrderedSet

From this point on, OrderedSet unambiguously refers to the one in BTree.

If this would still be ambiguous or sub-optimal in some files, you can create a Swift file to rename imports using typealiases:

// a.swift
import struct BTree.OrderedSet
typealias BTreeOrderedSet<T> = BTree.OrderedSet<T>

// b.swift
let foo = OrderedSet<Int>() // from Foundation
let bar = BTreeOrderedSet<Int>() // from BTree

There was a new syntax discussed for Swift 3, but it fell through.

I renamed OrderedSet to SortedSet in the Swift 3 version of BTree, which should serve as a workaround while a possible language-level fix is being discussed/implemented.