From Al Islam, we have:
The Shi’a believe that the rank of Imamat (the position of a divinely-appointed leader) is higher than that of prophethood and messengership.
... Prophet Muhammad (S) is has the highest rank among mankind, and is the most virtuous creature of God and the most honored before Allah. The above belief does not undermine his position since Prophet Muhammad was an Imam during his time as well!
With the possibility of being both Prophet and Imam, it seems that in order to meaningfully consider the rank of Imam higher than the rank of Prophet, there would need to be non-Imam Prophets (otherwise all Prophets would be Imams anyway). Hence my question:
Question: Were there non-Imam Prophets as per Shia Islam?
I'm not sure if this is possible, because the Qur'an (2:136 and 3:84) instructs us to not distinguish between Prophets. If there were non-Imam Prophets, then Prophet Muhammad would have higher rank, thereby distinguishing between Prophets.