What is the difference between a Prophet and an Imam according to Shi'ite theology?

So, with my elementary readings in Shi’ite theology, specifically the Ithnā‘ashariyyah or the Twelver Shi'a branch, I couldn't differentiate between a Prophet and a Shi'ite Imam. - The Prophets are divinely appointed by Allah for a mission, so are the Imams. - The Prophets are divinely guided, so are the Imams . - The Prophets are infallible with respect to the religion, so are the Imams. - The Prophets are leader of the ummah and obedience to them is obligatory, so it is for the Imams. - The Prophets communicate with the angels, so do the Imams. - The Prophets performed miracles with the permission of Allah, so do the Imams. - The Prophets were revealed the things of the future by Allah, so it is for the Imams. - The Prophets have a higher rank/status compared to the average believer, so do the Imams. What are the differences between them then? Please clarify the misconceptions if any.