Difference between Swift’s hash and hashValue

hash is a required property in the NSObject protocol, which groups methods that are fundamental to all Objective-C objects, so that predates Swift.
The default implementation just returns the objects address,
as one can see in
NSObject.mm, but one can override the property
in NSObject subclasses.

hashValue is a required property of the Swift Hashable protocol.

Both are connected via a NSObject extension defined in the
Swift standard library in
ObjectiveC.swift:

extension NSObject : Equatable, Hashable {
  /// The hash value.
  ///
  /// **Axiom:** `x == y` implies `x.hashValue == y.hashValue`
  ///
  /// - Note: the hash value is not guaranteed to be stable across
  ///   different invocations of the same program.  Do not persist the
  ///   hash value across program runs.
  open var hashValue: Int {
    return hash
  }
}

public func == (lhs: NSObject, rhs: NSObject) -> Bool {
  return lhs.isEqual(rhs)
}

(For the meaning of open var, see What is the ‘open’ keyword in Swift?.)

So NSObject (and all subclasses) conform to the Hashable
protocol, and the default hashValue implementation
return the hash property of the object.

A similar relationship exists between the isEqual method of the
NSObject protocol, and the == operator from the Equatable
protocol: NSObject (and all subclasses) conform to the Equatable
protocol, and the default == implementation
calls the isEqual: method on the operands.