Do the six days of Shawwal's White Fasting count as making up for the days missed in Ramadan, or must the missed days be made up separately?

Whoever breaks their fast in Ramadan is obligated to make up for it after Ramadan and before the beginning of the next Ramadan. If one delays making up the fast without a valid excuse, knowing the impermissibility of the delay, they are obligated, in addition to making up the fast, to offer expiation by feeding one poor person for each day. Fasting the six days of Shawwal or the white days (Ayyam al-Bid) does not suffice for making up the missed fasts (qada'). The correct view is that it is not permissible to combine the intention of making up a fast with the intention of observing voluntary fasts, such as the six days of Shawwal or the white days. Therefore, whoever has done so must repeat the makeup fasts. However, for one who intended only to make up the fast and fasted in Shawwal or on the white days, it is hoped that Allah will grant them the reward of fasting the six days and the white days.