Just so its understood this would include just about any war prior to Vietnam War.

I could explain in detail for pages about this in terms of every war from the 1700's onto World War 2. For this though I'll just use WW2, and it depends on battlefield and theater of war.

One thing to understand about medical care anywhere, not just in war. Is the job of each medical professional. Whether it be EMT, corpman, army medic, etc. Is they are only trying to keep you alive long enough until you get to the next level of care. And then same thing repeated and repeated over and over again. Until you reach the final level of care being an actual hospital with skilled surgeons and doctors.

For instance, in the Pacific during WW2. Marines/Soldiers who were wounded on an island like Iwo Jima or Okinawa would be carried by stretcher, to a vehicle. Such as a jeep, M3 half track, etc. They would then drive the Marine/Soldier to an assembly area by the beach where they would then be loaded onto a boat or amphibious landing craft and then delivered to a hospital ship. During this whole process the wounded Soldier would have been under the care of several different medical specialist of varying degress of expertise.

If this was the moment in which a battle just started though. Like landing troops on a beach for the first time, and the troops were under heavy fire. Then there would be no evacuation. The priority would be to kill the enemy first. This is done even with terrorist drills in schools and federal buildings today. Police are trained not to help you even if you are bleeding out and screaming in pain. The priority of the police would be to kill the enemy. That is not to say a medic or corpman would not render medical attention on a battlefield to keep you stable long enough to eventually get evacuated. But there would be no evacuation at the moment in of itself.

Same goes for another situation such a airborne soldiers. Who are trained to go behind enemy lines and kill the enemy. Again, no evacuation because there is nowhere to go since they are surrounded by the enemy.

In other places like in Europe during WW2 there would be a logistical and medical area usually a mile behind the front lines. Where troops would be evacuated via vehicle and to also receive supplies. Which would usually consist of combat surgeons and such. If their wound still wasn't fixed they would just quickly go from each varying level of care needed. Whether it be the Battalion aid station or the main hospital for the entire Area of Operation.

Source: https://www.sarahsundin.com/hospitalization-in-world-war-ii-chain-of-evacuation/

If you would like to know about medical evacuations today I actually just met recently with US Air Force pararescue jumpers, and a couple of Army Medics. Just last week they were tasked with jumping into a remote area to save a hiker mauled by a bear. They parachuted in since a helicopter is a lot slower then a C-130.

The field ambulance is certainly the first thing to come to mind, but that was not always available. What was standard procedure when the unit was not motorized?