Recoil Operated vs. Gas Operated
The above diagram comes from a June 1942, Popular Science article introducing the US Army's new M1 Carbine. The diagram illustrates the difference in operating systems used by the new carbine and the Thompson M1A1 submachine gun.
While both systems show use the expanding propellant gases or the fired cartridge they use it in different ways. The M1 Carbine siphons of gas into is gas cylinder driving the piston and operating rod backwards. While in the Thompson the bolt is blown back by the pressure of the gas.
In actuality the diagram is incorrectly labelled, the Thompson's action is described as 'Recoil Operated' which would imply that the weapon's barrel and bolt move rearwards when firing. In fact the Thompson uses a simpler blowback action where the unlocked breech allows the pressure from the fired bullet to push the bolt back against a recoil spring. However, in a true recoil system the breech is locked during firing and it is the recoil of the weapon's bolt and barrel back unlocking the breech before returning forward.
Popular Science, June 1942 (source)