Put me on the list of inspectors who fail to grasp the concept.
210.19(A)(1)(b) states the conductor shall have an ampacity 125% of the continuous load
I think you mean 210.19(A)(1)(a) in the above. Here's both (a) and (b), from the 2017 NEC (easiest to copy and paste):
(a) Where a branch circuit supplies continuous loads or any combination of continuous and noncontinuous loads, the minimum branch-circuit conductor size shall have an allowable ampacity not less than the noncontinuous load plus 125 percent of the continuous load.
(b) The minimum branch-circuit conductor size shall have an allowable ampacity not less than the maximum load to be served after the application of any adjustment or correction factors.
A strict reading of the above, since the term ampacity as defined in Article 100 includes any adjustment or correction factors, yields two oddities: (1) part (b) is totally redundant, as 125% of the continuous load, plus 100% of the noncontinuous load, will always be greater than 100% of the load and (2) the phrase "after the application of any adjustment or correction factors" in part (b) is totally redundant, since the word ampacity implies that already.
Those are both clues that (a) is using the word ampacity improperly, and what it really means is "ampacity before application of any adjustment or correction factors." That should be written explicitly, but it is still implicit, given the use of the phrase in part (b) but not part (a). That understanding makes the two requirements distinct.
The intended difference is clearer in the version of the above requirement that appears in 690.8(B), see it for comparison. Apparently the CMP for Article 690 are better language crafters than the CMP for Article 210.
Don and I both submitted PIs for the 2023 NEC to fix this misuse of terminology in 210.19(A)(1)(a), but the CMP response was basically "not required, it already says that." Even though that is clearly wrong.
Cheers, Wayne