class LinkedList {
   public:
   int mydata;
   // etc..
 
   LinkedList *next;
};

std::vector<classtype> classvector_instance;

//company.hclass company{    public:              //..functions go here    protected:              vector themanagers(20);           // making vectors with room for 20, 50 and 50 in order              vector thecasuals(50);              vector thesalesstaff(50); };

 
class company {
 
   // ...
 
 
 
   protected:
 
   std::vector<managers> themanagers;
 
   std::vector<casuals> thecasuals;
 
   std::vector<salesstaff> thesalesstaff;
 
};
 
 
 
// eg.
 
themanagers.push_back(/*initalization data for constructor*/);

themanagers[index_var].member_data = whatever;

   protected:
       std::vector themanagers;
       std::vector thecasuals;
       std::vector thesalesstaff;

 string temptype;
 string object_name
 cout << "Please enter a UNIQUE name for this staff member object: ";
 cin >> object_name;
 cout << "Please enter the type of staff member you would like to create." << endl;
 cout << "Either 'casual', 'manager' or 'salesperson'. : ";
 cin >> temptype;
 cout << endl;
if (temptype == 'casual')
{
   casual object_name();
   thecasuals.pushback(object_name);
}
//... Repeat else if for the manager and salesperson types..

 string object_name

if (temptype == 'casual')

 
//.. client.cpp
 
 string temptype;
 string object_name
 cout << "Please enter a UNIQUE name for this staff member object: ";
 cin >> object_name;
 cout << "Please enter the type of staff member you would like to create." << endl;
cout << "Either 'casual', 'manager' or 'salesperson'. : ";
 cin >> temptype;
cout << endl;
if    (temptype == 'casual')
   casual object_name();
   thecasuals.add_casual(object_name);
}
//.. rest of the else ifs

 
void company::add_casual(casual casname)
{
   thecasuals.pushback(casname);
}

if    (temptype == 'casual')
{ // I think you missed this brace here.
   casual object_name; // Removed the brackets. 
                       // causal object_name() is a function called object_name that returns a causal object. 
                       // You want a instance of class causal.
   thecasuals.add_casual(object_name);
}
//.. rest of the else ifs