Difference between Heir Presumptive and Interrex

HEIR PRESUMPTIVE vs INTERREX: NOUN

Someone who will inherit only if no better choice for an heir is born.
See heir apparent.
An heir who stands to inherit the estate, title, or office of an intestate ancestor, but whose claim can be defeated if a relative who is closer to the ancestor is born prior to the ancestor's death.
A person who expects to inherit but whose right can be defeated by the birth of a nearer relative

A similar interim ruler, CEO etc.
An equivalent regent from the death of a Polish king till the election and enthronement of his successor.
An official in Ancient Rome, who acted as single head of state during the interregnum between two consulates.
An interregent, or a regent.
In ancient Rome, a regent; a magistrate who governed during an interregnum.

Succession, Peacock throne, Kingship, Dynastic, King, Prince consort, Princeling, Monarch, Figurehead, Prince regent, Coronation, Heir, Successor, Throne, Heir apparent

Election, Regnative, Superordination, Viceregent, Academic administrator, Minister of state, Chief of state, Prorector, Preconization, Member of parliament, Pontificality, Preconize, Apocrisiarius, Interregnum, Interregent

Succession, Peacock throne, Kingship, Dynastic, King, Prince consort, Princeling, Monarch, Figurehead, Prince regent, Coronation, Heir, Successor, Throne, Heir apparent

Election, Regnative, Superordination, Viceregent, Academic administrator, Minister of state, Chief of state, Prorector, Preconization, Member of parliament, Pontificality, Preconize, Apocrisiarius, Interregnum, Interregent

He is the son of Eliwood, the main character of Fire Emblem: The Blazing Blade, and heir presumptive of Pherae.
Frenchman, that he is not heir presumptive to another crown, and that he has previously taken the civic oath.
Prince Albert became King George VI and the young Princess Elizabeth became heir presumptive to the throne.
Known as "The Brat" in the Heraldic Circle, the Heir-presumptive lives up to her nickname.
Roger was made lieutenant of Ireland and was declared heir presumptive to the Crown.

Once the interrex found a suitable nominee to the kingship, he would bring the nominee before the Senate and the Senate would review him.