The oxygenated blood just sits there, and can sustain vital function for a time if the animal is not in fight-or-flight mode (likely due to shock.) A double-lung instantly works on both collapsing the lungs and causing the heart to beat faster, pushing blood out of the wound, into the lungs sacs/pleural space for asphyxiation, out of the wound channel, and keeping the body from restricting flow due to trauma response.
There is no blood pumping during a human heart-attack, either, but it's not instantly fatal, and while unconsciousness can quickly follow, the organs and brain can remain viable for a number of minutes because there is still blood (and the sugars) in/around the brain and organ. If that blood was actively pumped out, unconsciousness would arrive quickly due to lack of blood pressure and then death would occur marginally quicker as the body will keep the heart beating (and thus, draining) even during unconsciousness.
While both double-lung and heart shots are viable and terminal for sure, it's not a massive difference in actual death, even it one runs further.