What does that mean in practice, if anything?
It sure looks like Sheiks and Imans have religious authority over other Muslims. Am I misunderstanding their roles?
More like some Sheiks and Imams misunderstand their roles.
Being a Person who wears both titles, I can honestly say I have no more religious authority than the newest Muslim.
Sheik is a title of respect similar to the English Mister. It is used for a very wide range of people. I wear the title as a respect for my old age. I got it because I just happened to live longer than the other kids on the block.
It is alo a political title used to address Landowners, Tribal leaders, etc It is also a title given to those that have a high level of education. It can be used to address a person that has achieved a Ph.D or equal in Religious Studies. as such a Sheik is expected to have knowledge about Islam, but that does not give them any authority over anyone.
An Imam is the person who leads the daily obligatory prayers. Usually the oldest person in the community. They have no religious authority.
A Mufti (Mullah for Shia) has the legal authority to issue rulings on Islamic Jurisprudence. They are Lawyers and are to have a minimum of a PhD in Islamic Jurisprudence. Even there the rulings are opinions and not considered to be infallible
There are Religious Leaders among the Shi'ites but as I have very little knowledge about the Shi'ite I do not know the extent of their roles, just my own opinions which may be wrong.