[T]he Renaissance motet is a polyphonic musical setting, sometimes in imitative counterpoint, for chorus, of a Latin text, usually sacred, not specifically connected to the liturgy of a given day, and therefore suitable for use in any service. The texts of antiphons were frequently used as motet texts. This is the sort of composition that is most familiarly designated by the term "motet," and the Renaissance period marked the flowering of the form.
In essence, these motets were sacred madrigals. The relationship between the two forms is most obvious in the composers who concentrated on sacred music, especially Giovanni Pierluigi da Palestrina, whose "motets" setting texts from the Canticum Canticorum, the biblical "Song of Solomon," are among the most lush and madrigal-like of Palestrina's compositions, while his "madrigals" that set poems of Petrarch in praise of the Blessed Virgin Mary would not be out of place in church. The language of the text was the decisive feature: if it's Latin, it's a motet; if the vernacular, a madrigal.
Frankly, these days I could care less what anyone calls anything, so long as it sounds good.
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