What is the NSObject isEqual: and hash default function?

As you’ve correctly guessed, NSObject‘s default isEqual: behaviour is comparing the memory address of the object. Strangely, this is not presently documented in the NSObject Class Reference, but it is documented in the Introspection documentation, which states:

The default NSObject implementation of isEqual: simply checks for pointer equality.

Of course, as you are doubtless aware, subclasses of NSObject can override isEqual: to behave differently. For example, NSString‘s isEqual: method, when passed another NSString, will first check the address and then check for an exact literal match between the strings.