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nil: A null pointer to an Objective-C object.
( #define nil ((id)0) )

Nil: A null pointer to an Objective-C class.

NULL: A null pointer to anything else.
( #define NULL ((void *)0) )

NSNull: A class defines a singleton object used to represent null values in collection objects (which don't allow nil values).

[NSNull null]: The singleton instance of NSNull.

Technically they're all the same,,, but in practice they give someone reading your code some hints about what's going on; just like naming classes with a capital letter and instances with lowercase is recommended, but not required.

If someone sees you passing NULL, they know the receiver expects a C pointer. If they see nil, they know the receiver is expecting an object. If they see Nil, they know the receiver is expecting a class. Readability.

example 1:

[NSApp beginSheet:sheet
              modalForWindow:mainWindow

              modalDelegate:nil //pointing to an object

              didEndSelector:NULL //pointing to a non object/class

              contextInfo:NULL]; //pointing to a non object/class

example 2: The values1 will only have obj1,
NSObject *obj1 = [NSObject new];
NSObject *obj2 = nil;
NSObject *obj3 = [NSObject new];
NSArray *values1 = [NSArray arrayWithObjects:obj1,obj2,obj3,nil];

example 3: The values2 have 3 objects and the second object is instance of NUSNull
NSObject *obj1 = [NSObject new];
NSObject *obj2 = [NSNull null];
NSObject *obj3 = [NSObject new];
NSArray *values1 = [NSArray arrayWithObjects:obj1,obj2,obj3,nil];

about testing:
if obj is nil , [obj message] will return NO, without NSException
if obj is NSNull , [obj message will throw a NSException
testing NSNull: (NSNull *)obj == [NSNull null]