Fatal and incapacitating are very different things. What is fatal? It is a sliding slope.
What is fatal 10 minutes from medical care might not be fatal 5 minutes from medical care.
In terms of defense, damage and trauma that is enough to actualy force a person into incapacition immediately is far above what is fatal most of the time. Contrast this with willing incapacitation where the trauma, pain and shock of the injury causes the person to flee or fall as a subconscious/involuntary psycological reaction. Most are the later, but someone trained or otherwise in a different state of mind(perhaps due to drugs) can continue to will actions until the physical body ceases to function as long as the nerves upon which those functions travel are intact.
Depending on the injuries this can be seconds (before incapacitation, minutes before irreversable brain damage due to lack of oxygen), or minutes. A serious heart injury will usualy only be seconds before incapacitation. However if surgery was immediately undertaken on the spot (obviously it never would unless in a hospital) and the loss of blood pressure remedied by fixing the wound, while IV fluids were administered to make up for lost blood, what would 99% of the time a fatal wound could be survived. Since surgeries are not performed in the field this pretty much means anything that cannot be survived longer than an emergency response, and corrosponding arrival to the hospital is what you would call fatal. The emergency personel can more or less extend this window depending on the injury with IV making up for blood loss, and ventilators, pure oxygen making the most of limited breathing function, and other procedures mainly in line with trying to keep the circulatory system functioning even if artificialy until arrival. Then there is the time for assessment and prep, incisions etc.
So fatal is a hard assessment to make. Are you trying to determine fatal, or incapacitation? Unsurvivable fatal injuries to the heart will not immediately incapacitate. The loss of blood pressure, preventing circulation, and removing the blood already oxygenated in the blood through immediate heavy blood loss by serious damage to the heart will make them unconscious within a matter of seconds, but seconds is plenty of time to return fire if they were so inclined. Luckily the instinctive reaction is usualy to psycologicly incapacitate themselves due to shock. With total irreversable damage to the circulatory system, the brain will suffer permanent damage within 3 minutes, and be pretty much dead several minutes afterwards. Since there will still be some oxygen already present from the last moments of function, and some blood still oxygenated present, this window is increased because there is still oxygen present for the brain in minor quantities after circulation fails. But this only adds a short undetermined amount of time. However this is in determining fatal, the person will obviously be unconscious prior to that time passing. Thier survival will depend on what others do or do not do and the time frame it is done in.
It is not a video game where the person has a health bar and if that goes to 0 they are dead. However for contrast lets pretend it is. A person could drop into negative numbers and function at least a few seconds, or only drop to 50, and die minutes or hours later.
Also it depends on the medical fields ability to repair certain tissues. Technology is not yet advanced enough to replace certain tissues. So if too much tissue is missing, sewing it up obviously won't work that well. Can't really grab some artificial heart tissue to use as a patch, as the heart is a muscle. So any patch would be non functional tissue.
Now if an artificial heart was used the real heart would certainly die, so they wouldn't pick that option, for several reason, one is obviously they do not just have spare artifical body parts laying around, and the other is that policy would leave many people with artificial hearts and poorer qualities of life and low life expectancies that could have successfuly had the real heart repaired. When working with limited amount of time, what they decide they are going to do needs to be right, as once in the middle of the procedure there will usualy not be enough time to change courses.
They did an open thoracotomy right there in resus and managed to get the knife out and sew up the guy's heart. I don't recall which chamber was involved, but I remember it was perforated good and proper. The guy survived though, with rapid intervention.
Keep in mind the guy survived long enough for this procedure because the knife kept the wound small by plugging the very injury it created. Had the knife been pulled out he would have likely not survived. However had the knife been left in and been disturbed even more serious injury would be created. So he was lucky.
So what is the real question? Fatal as in eventualy dead? Fatal as in immediately not a threat to you? (which is not necessarily fatal.)
Or incapacitated? Are you thinking of this in a shooting situation from your perspective as the person inflicting damage and what wills top the threat, or really care more about whether the injury will certainly cause death at some point?
Now imagine every tool, life support and artificial part was available in some fantasy hospital for every situation, and they had the insight to know the extent of the injuries. They could replace, or sew up the heart, get it going, sew together the arteries, sew in tubes where the artieries were missing and fix surely fatal injuries, and if done prior to the patient's brain going too long without oxygen, have them recover. However a week later these tubes could be rejected by the body or one come loose or tear, the heart be rejected, and the person then die from complications resulting from the injury.
The same can be said for minor heart related injuries. The heart is a well tuned muscle, nicks and cuts or scrapes can interfere with the proper function of that muscle at a later date. So perhaps the person will die at a later time from a heart attack cause by an irregularity brought on by the scar tissue from the wound. Does that qualify as fatal?