Electrical breakers question
Both conductors can carry the maximum current. However, since it can either be a 240V circuit or a 120/240V circuit, it can seem a bit confusing. At no time will you be able to draw more than the max current, but it is possible to have the maximum current on both conductors.

In all cases, both ungrounded conductors will have to be rated to carry the maximum current.  

Also note that the conductors only carry the current drawn by the loads attached. So the conductors will carry anywhere from 0 to the maximum current, depending on the demand of the loads.