The damage model as I understand it. Damage is based on the bullet and the bullet’s energy at impact. You can see the expected energy at impact when aiming with hunter sense on.
It shows about 5800 joules of energy with 338 at 100 meters. In the harvest screen we can look at what this shot did to the animal.
We can see when the bullet contacts the animal with almost 5900 joules of energy and it goes down as it moves through the animal. At 54 the top of the stats the 5900 is split between penetration and cavity damage. As I understand, penetration is the bullet path and cavity is the wound channel created. Each of the bar graphs show where that damage went. Any bar when full will add the blood icon to the left like the flesh one here. If you do considerably more damage, you will hit the skull icon like the left lung here. Either icon means the animal will die. The skull means instant death; blood drops means it will bleed out. The different bars take different amounts of damage to fill. Flesh or bones take a lot more than lungs or brain. You can adjust the colors in settings of the bar info in settings. For me, the green is set to penetration and white to cavity. You can see a gray section in flesh, this was from a previous shot, so the game does keep track of all damage to this animal. Once an animal is spawned on your map, they are there until you kill them or they die of old age. We can see in the bullet cam screen that the 338 did massive cavity damage that is not shown on the 55 stats. That is because it is mostly in the full bars of flesh and lungs, but since those bars are full it cannot show the extra damage to that organ.