Usando PHP MYSQLi cómo obtener solo deudores y solo acreedores administrados con action_type DR y CR

Parece que simplemente necesita modificar su HAVING cláusula, para filtrar los casos en los que balance es mayor que cero (Deudor) O balance es menor que cero (Acreedor).

También puede usar condicional IF() expresiones para determinar dr/cr en el balance columna.

Para conseguir Deudores solo:

SELECT client_id, 
       Sum(Coalesce(CASE 
                      WHEN action_type = 'dr' THEN amount 
                    end, 0)) AS total_debits, 
       Sum(Coalesce(CASE 
                      WHEN action_type = 'cr' THEN amount 
                    end, 0)) AS total_credits, 
       Sum(Coalesce(CASE 
                      WHEN action_type = 'cr' THEN amount 
                    end, 0)) - Sum(Coalesce(CASE 
                                              WHEN action_type = 'dr' THEN 
                                              amount 
                                            end, 0)) AS total_debtors, 
       IF(Sum(Coalesce(CASE 
                         WHEN action_type = 'cr' THEN amount 
                       end, 0)) - Sum(Coalesce(CASE 
                                                 WHEN action_type = 'dr' THEN 
                                                 amount 
                                               end, 0)) > 0, 'dr', 'cr') AS balance 
FROM   tbl_balancesheet 
GROUP  BY client_id 
HAVING balance = 'dr' AND total_debtors <> 0

Para obtener acreedores solo:

SELECT client_id, 
       Sum(Coalesce(CASE 
                      WHEN action_type = 'dr' THEN amount 
                    end, 0)) AS total_debits, 
       Sum(Coalesce(CASE 
                      WHEN action_type = 'cr' THEN amount 
                    end, 0)) AS total_credits, 
       Sum(Coalesce(CASE 
                      WHEN action_type = 'cr' THEN amount 
                    end, 0)) - Sum(Coalesce(CASE 
                                              WHEN action_type = 'dr' THEN 
                                              amount 
                                            end, 0)) AS total_debtors, 
       IF(Sum(Coalesce(CASE 
                         WHEN action_type = 'cr' THEN amount 
                       end, 0)) - Sum(Coalesce(CASE 
                                                 WHEN action_type = 'dr' THEN 
                                                 amount 
                                               end, 0)) > 0, 'dr', 'cr') AS balance 
FROM   tbl_balancesheet 
GROUP  BY client_id 
HAVING balance = 'cr' AND total_debtors <> 0