From the Swift blog:

This feature was first released in Xcode 6.3 with the keywords __nullable and __nonnull. Due to potential conflicts with third-party libraries, we’ve changed them in Xcode 7 to the _Nullable and _Nonnull you see here. However, for compatibility with Xcode 6.3 we’ve predefined macros __nullable and __nonnull to expand to the new names.

From the clang documentation:

The nullability (type) qualifiers express whether a value of a given pointer type can be null (the _Nullable qualifier), doesn’t have a defined meaning for null (the _Nonnull qualifier), or for which the purpose of null is unclear (the _Null_unspecified qualifier). Because nullability qualifiers are expressed within the type system, they are more general than the nonnull and returns_nonnull attributes, allowing one to express (for example) a nullable pointer to an array of nonnull pointers. Nullability qualifiers are written to the right of the pointer to which they apply.

and:

In Objective-C, there is an alternate spelling for the nullability qualifiers that can be used in Objective-C methods and properties using context-sensitive, non-underscored keywords

So for method returns and parameters you can use the the double-underscored versions __nonnull/__nullable/__null_unspecified instead of either the single-underscored ones, or instead of the non-underscored ones. The difference is that the single and double underscored ones need to be placed after the type definition, while the non-underscored ones need to be placed before the type definition.

Thus, the following declarations are equivalent and are correct:

  
    - (nullable NSNumber *)result
- (NSNumber * __nullable)result
- (NSNumber * _Nullable)result

For parameters:

- (void)doSomethingWithString:(nullable NSString *)str
- (void)doSomethingWithString:(NSString * _Nullable)str
- (void)doSomethingWithString:(NSString * __nullable)str

For properties:

@property(nullable) NSNumber *status
@property NSNumber *__nullable status
@property NSNumber * _Nullable status

Things however complicate when double pointers or blocks returning something different than void are involved, as the non-underscore ones are not allowed here:

- (void)compute:(NSError *  _Nullable * _Nullable)error
- (void)compute:(NSError *  __nullable * _Null_unspecified)error;
// and all other combinations

Similar with methods that accept blocks as parameters, please note that the nonnull/nullable qualifier applies to the block, and not its return type, thus the following are equivalent:

- (void)executeWithCompletion:(nullable void (^)())handler
- (void)executeWithCompletion:(void (^ _Nullable)())handler
- (void)executeWithCompletion:(void (^ __nullable)())handler

If the block has a return value, then you're forced into one of the underscore versions:

- (void)convertObject:(nullable id __nonnull (^)(nullable id obj))handler
- (void)convertObject:(id __nonnull (^ _Nullable)())handler
- (void)convertObject:(id _Nonnull (^ __nullable)())handler
// the method accepts a nullable block that returns a nonnull value
// there are some more combinations here, you get the idea

As conclusion, you can use either ones, as long as the compiler can determine the item to assign the qualifier to.