The long hadeeth of the Intercession is reported by al-Bukhaaree (Eng. trans., vol. 6, no. 236) and Muslim (Eng. trans., vol. 1, pp.122-135).
Concerning the types of intercession, Shaikh Abdul-Azeez ibn Baaz (rahimahullaah) says, in his notes on al-Aqeedah al-Waasitiyyah (p.73), The different intercessions that will occur on the Day of Resurrection are six and are well-known from the Shareeah proofs. From them, three are particular to the Prophet. The six types are:
i) The Major Intercession, which is for judgement to commence for those gathered for it; ii) Intercession for the People of Paradise to enter it; iii) His intercession for the punishment to be lightened for his uncle, Abu Taalib, so that he is placed in a shallow part of Hell-Fire. This form of intercession is particular to the Prophet for his uncle Abu Taalib. As for other disbelievers, there is no intercession for them. He, the Most High, said:
So no intercession of intercessors will be of any use to them. Soorah al-Mudathir (74): 48
iv) Intercession for some of those who deserve the Fire not to enter it; v) Intercession for those who enter the Fire to come out of it; vi) His intercession for the raising of the ranks of the people of Paradise. This last intercession is general for the Prophet and other Prophets, the righteous, the angels and for Muslim children who died whilst they were young.
All of these are only for the people who were upon Tawheed. As regards the sinful from the people of Tawheed who enter the Fire, they will not remain in it, but will be brought out after being purified. It is established in the Saheeh from the Prophet that the sinful will die in it, and then they will be brought out like charcoal. Then, they will sprout (in Paradise) like shoots upon a riverbank.