One way is to classify it based on the heat input.
Normally HRSG's do not have any additional heat input. The performance and output of the HRSG is dependent on the exhaust heat of the gas turbine. At part loads, this leads to reduced output from the HRSG's. In addition, ambient conditions also affect the Gas Turbine performance. This could affect the downstream process were the steam is used. To avoid such situations supplemental firing of oil or gas takes place. Even though this may not be an efficient process, it avoids costly production disturbances.
Supplemental Firing takes place in burners in the gas duct at HRSG inlet. Oil or gas is the supplementary fuel. Since the flue gas at exhaust of a Gas Turbine is high in Oxygen content, additional air is not required for combustion. This eliminates the need of Forced draft or Induced Draft fans.