وَمَنْ كَانَ مَرِيضًا فِي رَمَضَانَ، فَخَافَ إِنْ صَامَ ازْدَادَ مَرَضُهُ: أَفْطَرَ، وَقَضَى.
Translation: Whoever is ill in Ramadan and fears that fasting will worsen his illness may omit the fast and subsequently make it up.
The relevant condition is a credible fear that fasting will worsen the illness, not the mere existence of an illness label. In that case the person may break or omit the fast and later makes it up.
The two verbs carry different functions: afṭara concerns the present concession, whereas qaḍā indicates performance of the missed fast later.