ANSWER:
No, the kaffarah is not the same as it is only for intercourse during the day time of Ramadan. She must only keep that fast again.
If he forced her and she was not willing all the time, her fast is valid.
https://islamqa.info/en/answers/40242/does-expiation-have-to-be-offered-for-having-intercourse-when-making-up-a-missed-ramadaan-fast