These are names for how a hadith book is organised, not grades of authenticity. A Jami' covers every area of the religion — creed, rulings, tafsir, manners, trials and virtues — as in Sahih al-Bukhari (whose full title is al-Jami' al-Sahih) and Jami' al-Tirmidhi; a Sunan is arranged by the chapters of fiqh and concentrates on legal rulings, as in the Sunan of Abu Dawud, al-Nasa'i and Ibn Majah. A Musnad groups narrations under the name of each Companion who narrated them rather than by subject, as in Musnad Ahmad, while a Musannaf is arranged by topic but also includes alongside the marfu' reports the statements of the Companions and Tabi'un, as in the Musannaf of Ibn Abi Shaybah and that of 'Abd al-Razzaq. The crucial point is that apart from the two Sahihs, these works were not written to contain only authentic material, so every report in them still needs an individual grading.
Q&A · Hadith
What is the difference between a Jami', a Sunan, a Musnad, and a Musannaf?
Evidence — the daleel
Sahih al-Bukhari (al-Jami' al-Sahih)Jami' al-TirmidhiSunan Abi DawudMusnad Ahmad ibn HanbalMusannaf Ibn Abi ShaybahMusannaf 'Abd al-Razzaq
On deen2u
Informational, not a personal fatwa. Consult a qualified scholar for rulings on your situation.