Cable selection is two tests, and you take whichever gives the bigger conductor. Current-carrying capacity protects the cable from itself. Voltage drop protects the load from being undersupplied.
On short runs the current rating usually decides. On long runs voltage drop almost always decides, and by a wide margin — which is why a 20 A circuit at the end of a 40 m run can need a cable two or three sizes larger than the breaker suggests.