A hadith referred back to the Prophet, e.g. a reporter (whether a Companion, Successor or other) says, "The Messenger of Allah said ..."
A hadith referred back to a Companion, e.g. "Ibn 'Abbas said ...", without being attributed to the Prophet.
A hadith referred back to a Successor, e.g. "Al-Hasan al-Basri said ..."
The authenticity of each of these three types of hadith depends on other factors such as the reliability of its reporters, the nature of linkage among them, etc. However, the above classification is extremely useful since through it the sayings of the Prophet can be distinguished at once from those of Companions or Successors; this is especially helpful in debate in matters of fiqh.
Imam Malik's al-Muwatta', one of the early collections of hadith, contains a relatively even ratio of these types of hadith, as well as mursal ahadith (which are discussed below). According to Abu Bakr al-Abhari (d. 375), al-Muwatta' contains the following:
600 marfu' ahadith, 613 mauquf ahadith, 285 maqtu' ahadith, and 228 mursal ahadith; a total of 1726 ahadith.
Among other collections, relatively more mauquf and maqtu' ahadith are found in al-Musannaf of Ibn Abi Shaiba (d. 235), al-Musannaf of 'Abd al-Razzaq (d. 211) and the Tafsirs of Ibn Jarir (d. 310), Ibn Abi Hatim (d. 327) and Ibn al-Mundhir (d. 319).