NSMutableString *s;
…
-(void)functionA:(NSString *)string {
[self.s appendString: string];
}

-(void)functionB:(NSString *)string {
NSString* c = self.s;
NSString* c = [NSString stringWithString: self.s];
}

“Returns a string created by copying the characters from another given string.”

self.s is a refernce to s, might change over time, stringWithString makes a copy, a “snapshot” of self.s…