A gamma sterling engine (picture edited from one found Here)
Their are three main types of sterling engines, alpha beta and gamma.
Alpha Sterling Engine
Alpha sterling engines have two connected pistons with sealed heads. The high temperature heat exchanger is attached to one piston and the cold heat exchanger is attached to the other cylinder. Usually a regerator is attached between the cylinders.
Beta Sterling Engine
The beta sterling engine has a single cylinder that contains two pistons and a hot and cold heat exchangers. The power piston is tight fitting and changes the volume of the cylinder. The displacer piston is loose fitting and moves the gas from the hot end to the cold end and from the cold end to the hot end.
Gama Sterling Engine
The gamma Sterling engine is similar to the alpha sterling engine except it has two cylinders one for the displacer piston and one for the power piston. The hot and cold heat exchangers are located on opposite sides of the cylinder with the displacer piston. The gamma Sterling engine often has a lower compression ration then the beta sterling engine but it is much easier to build because the connecting rods for the pistons don't exit at the same spot.