You are close.
Facism is a method of governing. Wikipedia defines it as "Fascists seek to unify their nation through a totalitarian state that seeks the mass mobilization of the national community through discipline, indoctrination, and physical training"
Corporatism is an economic system. Under Corporatism, corporations are privately owned, they are strong-armed by regulations and quotas to the point that they are essentially controlled by the government. It is a form of socialism.
Both facism and corporatism are aspects of the Nazi party.
But corporatism is a mutually beneficial arrangement - the regulations and quotas are deemed a small price to pay in return for the guaranteed market monopolies, government contracts, and indemnification from the laws of capitalism the larger corporations get in return. This is why the likes of GE and Monsanto are going the IG Farben route and enthusiastically supporting Obama's budding dictatorship.
Smaller businesses, on the other hand, get all of the regulations with none of the guarantees.