The Minister for Magic is an office in the Harry Potter continuum which serves the Wizarding World in a role similar to the Prime Minister.
This office is known as that of the 'Minister of Magic' in the American versions of the books.
An incompetent who is often bullied in Suefics, as the Sues don't seem to realize that, for all his ineptness, he DOES have power.
Fudge's successor, who is NOT an incompetent. He is killed in Deathly Hallows during the Ministry of Magic takeover by the Death Eaters.
Thickneese was the Minister for the majority of Deathly Hallows. He was actually a puppet minister during Voldemort's regime and kept under control via the Imperius Curse.
The Minister of Magic post-Voldemort and an Order of the Phoenix member.