The difference between Mayor and Provost

Mayor as a noun:

The leader of a city, or a municipality, sometimes just a figurehead and sometimes a powerful position. In some countries, the mayor is elected by the citizens or by the city council.

Mayor as a noun (historical):

The steward of some royal courts, particularly in early Medieval France

Provost as a noun (religion, historical):

One placed in charge: a head, a chief, particularly: A dean: the head of a cathedral chapter. The head of various other ecclesiastical bodies, even muezzins. The minister of the chief Protestant church of a town or region in Germany, the Low Countries, and Scandinavia. The head of various colleges and universities. A ruler. A mayor: the chief magistrate of a town, particularly the head of a burgh or the former chiefs of various towns in France, Flanders, or other Continental European countries.

Provost as a noun (religion, historical):

A senior deputy, a superintendent, particularly: A prior: an abbot's second-in-command. A senior deputy administrator; a vice-president of academic affairs. A steward or seneschal: a medieval agent given management of a feudal estate or charged with collecting fees; a title of the archangel Michael. Any manager or overseer in a medieval or early modern context. A viceroy. A governor. A reeve. Various Roman offices, as prefect and praetor. A constable: a medieval or early modern official charged with arresting, holding, and punishing criminals. An officer of the military police, particularly provost marshal or provost sergeant. An assistant fencing master.

Provost as a noun (UK, military, _, slang, obsolete):

A provost cell: a military cell or prison.

Provost as a verb (UK, transitive, used in passive, obsolete, military, _, slang):

To be delivered to a provost marshal for punishment.