read this article http://objc.tanb.me/issues/nsobject_copy/ (Japanese version only)

gistfile1.m

    NSObject *obj = [NSObject new];
    NSObject *copyObj = [obj copy];

gistfile2.m

    NSString *str = @"Hello... Hello... Hello...";
    NSString *copyStr = [str copy];
    // these are same address.
    NSLog(@"%p, %p", str, copyStr);
    
    NSMutableString *mutableStr = [str mutableCopy];
    NSString *copyMutableStr = [mutableStr copy];
    // these are not same.
    NSLog(@"%p, %p", mutableStr, copyMutableStr);

    NSString *copyCopyMutableStr = [copyMutableStr copy];
    // these are same
    NSLog(@"%p, %p", copyMutableStr, copyCopyMutableStr);

gistfile3.m

    NSMutableString *copyMutableStr = [mutableStr copy];
    // this raise NSInvalidArgumentException
    [copyMutableStr appendString:@"append"];

gistfile4.m

    NSArray *arr = @[@"hello", @"こんにちは"];
    NSArray *copyArr = [arr copy];
    // these are same
    NSLog(@"%p, %p", arr, copyArr);
    // contens addresses are same.
    NSLog(@"arr's contents");
    [arr enumerateObjectsUsingBlock:^(id obj, NSUInteger idx, BOOL *stop) {
        NSLog(@"%p", obj);
    }];
    NSLog(@"copyArr's contents");
    [copyArr enumerateObjectsUsingBlock:^(id obj, NSUInteger idx, BOOL *stop) {
        NSLog(@"%p", obj);
    }];
    
    NSMutableArray *mutableArr = [arr mutableCopy];
    // these are not same
    NSLog(@"%p, %p", arr, mutableArr);
    // but content addresses are same.
    NSLog(@"arr's contents");
    [arr enumerateObjectsUsingBlock:^(id obj, NSUInteger idx, BOOL *stop) {
        NSLog(@"%p", obj);
    }];
    NSLog(@"mutableArr's contents");
    [mutableArr enumerateObjectsUsingBlock:^(id obj, NSUInteger idx, BOOL *stop) {
        NSLog(@"%p", obj);
    }];

gistfile5.m

    NSData *archived = [NSKeyedArchiver archivedDataWithRootObject:arr];
    NSArray *deepCopyArr = [NSKeyedUnarchiver unarchiveObjectWithData:archived];
    // these are not same
    NSLog(@"%p, %p", arr, deepCopyArr);
    NSLog(@"deepCopyArr's contents");
    [deepCopyArr enumerateObjectsUsingBlock:^(id obj, NSUInteger idx, BOOL *stop) {
        NSLog(@"%p", obj);
    }];