Ampacity is defined in article 100 as "The current, in amperes, that a conductor can carry continuously under the conditions of use without exceeding its temperature rating".
Notice this says "conductors". Overcurrent protection (breakers or fuses) are not mentioned.
Now lets go look at the common conductors used on circuits used for general lighting, 12ga and 14ga. If I look an article 315, I see a 14ga conductor is 20a and a 12 ga conductor is 25a (in the 60c column, the strictest category). OK so where does the 20a and 15a standard come from? That is in 240.4(D) where they tell you what breakers size you should use on "small conductors". With a few exceptions mostly where motors or welders are involved, you have that limit we know and love. Since the installer has no control over what a user will plug in, they build that 80% safety factor into the maximum breaker allowed.
I have never seen that mythical "80% breaker" but I would be willing to look at a catalog that lists one. I am not sure why that would even exist since the NEC.
There are a lot of other rules about specific circumstances, motor loads, ambient temperatures etc but generally they will apply in industrial applications. Where the homeowner will usually see that is the conductors going to their A/C compressor. Uninformed home inspectors will write up a perfectly legal installation because the breaker does not seem to match the wire they used and they do not understand the label on the unit. They will be wildly wrong if they also try to apply "the 80% rule" to the breaker when the real rule is as much 250%.
Light your torches and flame away ;-)