I am confused regarding the kaffaarah of 60 days for intentionally breaking a fast during Ramadhaan.

Answer

There is no conflict. You have confused Ramadhaan qadha with fasts which are kept during the month of Ramadhaan. If a person makes niyyat (intention) during the night time (i.e. before Subh Saadiq/Fajr time) to fast the next day of Ramadhaan, and he breaks this fast without valid reason, he is liable for the 60 day Kaffaarah penalty. This penalty applies if the fast is broken during the month of Ramadhaan. However, if one had not fasted for some reason during Ramadhaan, then one has to make Qadha of the missed fast. This Qadha will obviously be made after Ramadhaan. If a person begins the day making qadha of his fast, and then breaks this Qadha fast intentionally without valid reason, the 60 day penalty does not apply to this qadha fast. He still has to make only one qadha fast. The penalty applies only when breaking intentionally a fast during the month of Ramadhaan.