wa alaykum salam wa rahmatuLlahi wa barakatuHu,
There are two different kaffarahs discussed by our scholars. They are:
(1) Kaffarah kubra [major expiation, at times also called kaffarah ‘uzma], which is specific to intercourse [jima’] during a Ramadan fast day.
(2) And there is kaffarah sughra [minor expiation]. In Hashiyat al-Tarmasi 5\737, it is mentioned that this is also called fidyah or kaffarah mukhaffafah. It is giving a measure of foodstuff to the poor.
In the Madhhab there is a difference of opinion of if one breaks the fast by something besides intercourse and if then kaffarah sughra needs to be given. In Sharh al-Muhadhdhab 6\293 and Rawdah 2\267, Imam Nawawi related this difference and stated that the relied-upon opinion is that fidyah is not due along with the make-up fast.
He related that the ‘Iraqis held only one opinion on the matter (i.e. that no fidyah is due), and that this is the position maintained by the majority of the Khurasanis too. While also, the Khurasanis related the issue as one of wajhayn, thus relating an opinion that fidyah is necessary. The view that it is necessary takes into consideration that the breastfeeding women and the pregnant women are excused from fasting and still must pay it, thus an unexcused individual must pay it bil-awla [by stronger reason]; Bandiniji transmitted this from Ibn Abi Hurayrah.