Comparing Strings in Cocoa
First of all, you are using the == operator to compare two object pointers (of type NSString *). So that returns true when the pointers are the same, not when the strings have the same contents. If you wanted to compare whether two strings are the same, you should use isEqualToString: or isEqual: (isEqual: is more general as it works for all types of objects).
Second, compare: returns 0 (NSOrderSame) when they are the same, and 1 (NSOrderedDescending) when the first is greater than the second. So in fact it returns 1 only when they are different (specifically, when the first is greater than the second).
When comparing two identical strings compare will return NSOrderedSame, which is 0. It can also return NSOrderedAscending, -1, and NSOrderedDescending, 1.
You may prefer to use isEqualToString which returns YES or NO.