Shouldn't we use pointer here

Question

class myClass {
public:
myClass() {
cout <<"Hey";
}
void setName(string x) {
name = x;
}
string getName() {
return name;
}
private:
string name;
};

the setName function permanently sets the value of the string - name to string - x. why is this not similar to putting argument by value (and not by reference) in function, when in that case the string called name shouldn't have been modified permanently.