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?

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?