The Thermactor is the air pump, fresh air into the exhaust system,
EGR is exhaust gas recirculation.
They are pretty independent of each other, but keep in mind, everything on modern engines is interrelated.
The air pump pumps fresh air into the exhaust, and it helps burn off unburnt hydrocarbons
and convert CO to CO2, in the catalytic converter.
EGR is used mainly to reduce oxides of nitrogen, from the engine. It can also be used in some conditions to reduce spark knock.