The Hadith you are referring to has been mentioned in the Sunni and Shia books and there are differing opinions about its authenticity. Clearly, people from each sect will use it to claim they are the one that will be saved. Yet, there is no question that all of the 73 sects will be “Muslim”, if in fact the Hadith is correct. Thus, the ones who will be saved will depend on who follows the Prophet (sawa) properly. This means complete adherence to the Holy Quran and the Ahl al-Bayt, irrespective of calling oneself Sunni or Shia.
The issue of Muslims going to hellfire is a separate discussion. There are verses of Quran and traditions that indicate that some Muslims will be punished for a certain time and then allowed into paradise. Yet, the only one who knows is Allah