Prince Sultan retains the title of Crown Prince (at least for the moment) and the position of First Deputy Prime Minister.
Prince Nayef has been appointed Second Deputy Prime Minister, making him second in line to the throne after Crown Prince Sultan.
This is what Wiki
has to say about Prince Nayef:
HRH Prince Naif/Nayef bin Abdul Aziz (born 1933): The Second Deputy Prime Minister of Saudi Arabia. He is one of the six surviving members of the Sudairi Seven, all sons of King Ibn Saud and Hassa bint Ahmad Al Sudairi, which includes the Crown Prince.
Prince Nayef implemented the Al Saud decision to begin issuing women with identity cards in November 2001. The Directorate of Civil Status issued the first ID to women, thus making it much easier for women to carry out transactions - financial, legal and social - and is therefore considered a highly significant move. Previously women were registered on their husband's or father's ID cards.