Is it sufficient, according to the Shafi'i school, for someone who has broken their fast in Ramadan for years without a valid excuse to only offer fidyah? And what is the difference between fidyah and kaffarah?

The Shafi’is hold that delaying the make-up of Ramadan (definition) fasts without a valid excuse does not negate their obligation. Whoever delays the make-up without an excuse until the next Ramadan begins must feed a needy person one mudd of food for each day. The sounder opinion among them is that the fidyah (definition) (expiatory feeding) is repeated with the repetition of the years. So, whoever delays the make-up until another Ramadan without an excuse is obligated to fast the present Ramadan, then make up the missed Ramadan fasts, along with feeding a needy person for each day. If the years repeat, the fidyah also repeats.