I've been preparing for an interview, and I've seen both of these phrases used when introducing yourself and thanking someone for their time or when support is being given. For example:

お忙しいなかお時間をとって いただきありがとうございます

お忙しいところ大変恐縮ではございますが、何卒よろしくお願いいたします

Is there a nuanced difference between using ところ and なか in this kind of situation, or are they generally interchangeable? As well, what is the direct translation of ところ・なか?