Cause and effect

what would the cause be of a vehicle not starting from the effect of overheating?

“Not starting” could mean that the engine is cranking but not running under its own power, or it could mean that the engine will not even crank when the ignition key is turned.

In the absence of an explanation of “not starting”, some possibilities are:
Badly warped heads and/or damaged cylinder walls that will not hold compression, bad bearings, melted pistons, etc, etc.

Your question is, “What damage does overheating do which prevents engine start?”.
One thing could be warped valves which don’t allow compression. Another is: the piston rings have carved the cylinder walls.
Someone who has torn down such an overheated engine will have observations of damages which prevent start. Right?

Again it all depends on more information, but you could be describing overheating the high voltage ignition (spark) system.

Let’s step back. What are the symptoms of the overheat?

Warped or cracked cylinder heads or engine block not holding any compression, seized piston rings, fried valves, etc. etc…

It cranks but doesn’t catch to run on its own.

It’s getting the spark, but for the overheating was that as soon as I noticed the temperature gauge was going into the red I pulled over to let it cool down and to fill up the engine coolant. After that I tried to start the car but it wouldn’t.

The temperature gauge was in the red and steaming.

So I would have to get the motor tore down to really find out what the problem is?

Well, you could get a cylinder compression gauge tester that screws in the spark plug hole to determine if the cylinders are getting compression. You install the gauge one cylinder at a time, crank the engine over a few times, and write down the pressure that the gauge reads. reset the gauge between cylinders, and collect readings from all four. Then, check to make sure all the reads are within 10% of each other. Typical good pressure readings are in the 140 psi or better range. Readings of 90 psi are common in worn engines. less than that, and it probably is not enough to run. Then, you’ll need to tear it down.

But first, check to be sure it is getting spark (by removing a spark plug so you can observe it while the engine is cranked) and also getting fuel. (See if it responds to a shot of starting fluid). Then the compression test…

There are degrees of overheating. If the condition went undetected for a while, and the driver did not notice until it started making a lot of noise or just quit, few aluminum engine cars survive this…

The engine started to run rough. You saw the temperature gauge go into the red, and the engine started steaming. You found the coolant level low, and then, the engine wouldn’t start. Those are the events, aren’t they?
You need to try to find out what is wrong with the engine before you try to get it started, and run. The engine needs repair. That’s why it won’t start. To find out what repairs it needs, you need to do a cooling system pressure check. The coolant leak may be internal, or external. A compression test is also needed.
The engine might have a leaking cylinder head gasket, or a leak somewhere else. The coolant pressure test will reveal where.