The term Prince of the Church is today used nearly exclusively for Catholic cardinals. However, the term is historically more important as a generic term for clergymen whose offices hold the secular rank and privilege of a prince (in the widest sense) or are considered its equivalent. In the case of Cardinals, they are always treated in protocol of Catholic countries as equivalents of royal princes.
Informally, other members of the higher hierarchic echelons of the Catholic church are in recent times also occasionally called "Princes of the church", in which case this title can sometimes be intended more or less ironically by the speaker.
Every Cardinal of the Roman Catholic Church is still called a Prince of the Church because their College of Cardinals elects a new Pope (de facto from their number) during a period sede vacante in a special session called a conclave, where an age-limit applies. The Cardinals thus are an ecclesiastical equivalent to the Prince-electors of the former Holy Roman Empire, the other major elective monarchy in European history. The title carries no sovereign authority.
For analogous positions in non-Roman Catholic, and especially non-Christian contexts, the term Prince of the Faith is used.
In Hindu regions of the Indian subcontinent, the priestly caste of Brahmans ranks higher than the noble caste of Kshatriyas. As a result, princes of the faith can be considered the de jure superiors to princes of the blood. However, the two groups often competed with one another for de facto sovereignty, and some historic figures in Indian history have held both sacred and secular titles. As real power usually lay with the secular rulers, many Brahmins sought social promotion by serving them, e.g. as spiritual advisers at court, and even with (non-Hindu) occupying colonial powers, often in administrative positions where their intellectual qualities could be harnessed.