The big & popular one is "headspace" we covered the intro to that in your other post. In practical terms its more of a reloaders problem than a shooters though.

Now we move forward of the rim.

NOTE nothing in front of the rim is in any way connected to headspace. These are rimmed cases & many conflate the two based on rimless cases.

Generous Chamber: An overall loose fit allowing foreign crud to be present without jamming up the gun. The brass just flops down in there.

Again a repository for foreign crud like trench mud. You'll usually see it in two variations, sometimes both at the same time. A different profile to the shoulder, round not conical, & space from base the shoulder is made closer to, or further from the base.

Throat: Not anything directly to do with the case. The Throat is the un-rifled beginning of the bare in front of the chamber. The bullet is designed to break it's seal with the case & then free "jump" into the "forcing cone" the tapered beginning of the rifling in the bore.

Look at fired & unfired cases (from the exact same gun) & you'll usually see evidence of both. Uneven radial expansion of the case just in front of the rim. It's normal unless there's a huge amount of it. A clue you have a problem would be cases fracturing at this point, but that also relates to Head space being excessive. If you gauge for head space & pass, or it fails & you fix it & it still happens after you fix that it is still there excessively the barrel (including the chamber is "shot out".

Cure for both, well neck sizing of the case is the popular one. Now were into "reloading world" again though.

Throat erosion. The free run area has been blasted with screaming hot flaming powder grains & has eroded away.

You replace the barrel.

BUT don't panic! This takes many, many thousands of rounds.

Test for it? (assuming you reload again) take a fired case. Gently punch 3 dimples equally spaced (more or less) around the neck. Manually push a bullet in backwards. Just enough to hold it. Now pull the trigger & hold it & slowly ease the bolt to close with your test in the chamber, making sure the bolt closes fully.

Carefully pull it out without letting it fall.

Measure the overall length.

Make a not of it.

Now compare that reading with good known readings from newish barrels.

If yours is a good bit longer (not tiny amounts) you throat is eroded.

This is actually a reloading illustration, but it does show the neck, shoulder & illustrate the differences.

Cases stretch in all rifles, its normal.

The L-E has a few unique "stretch marks" of its own though.

The eccentric radial one is one (& the rumors about what causes it are hilarious IMO) & the blown out case in front of the rim is another.

Test for it? (assuming you reload again) take a fired case. Gently punch 3 dimples equally spaced (more or less) around the neck. Manually push a bullet in backwards. Just enough to hold it. Now pull the trigger & hold it & slowly ease the bolt to close with your test in the chamber, making sure the bolt closes fully.

Carefully pull it out without letting it fall.

Measure the overall length.

Make a not of it.

Now compare that reading with good known readings from newish barrels.

If yours is a good bit longer (not tiny amounts) you throat

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Rather than gently punch 3 dimples around the case neck
couldn't I use my lee collet die set that I have never used to size the neck ?

I measured the cartridge OAL using the method Shamu gave when the BSA barrel was new in my No. 4, IIRC it measured 3.17 inches with a Sierra 174 gr MK. It now measures (using a proper throat gage) something like 3.65 inches, yup, the bullet is out of the case neck before it touches the lands. Accuracy was still very good until just recently.  I estimate 10,000 rounds thru the barrel now. 

If you’re still curious about this, get a Hornady throat gage.  Hornady also makes a .303 case that is threaded at the head to attach to the gage.