That's the right idea.
The way I would put it is that 230.42(a)(1) is the analogue of 210.19(A)(1)(a), and they and 110.14(C)(1) are about termination provisions. These sections use the ampacity table 310.16 just as a lookup for current to wire size, based on the termination temperature rating, and do not apply adjustment or correction.
Whereas 230.42(a)(2) is the analogue of 210.19(A)(1)(b) and is actually about ampacity as defined in Article 100 and calculated according to 310.14.
Similarly you have 215.2(A)(1)(a) vs (b) and 705.28(B)(1) vs (2), plus probably others. They are all saying the same thing, and I think 705.28(B) expresses the difference best. Note that in 705.28(B) the currents are considered continuous, so it just references 125% rather than 125% of the continuous portion plus 100% of the rest.
Cheers, Wayne