Definition
Here, generalizing from the term most commonly employed in French, I will use the word preface to designate every type of introductory (preludial or postludial) text, authorial or allographic, consisting of a discourse produced on the subject of the text that follows or precedes it. The “postface” will therefore be considered a variety of preface; its specific features – which are indisputable – seem to me less important than the features it shares with the general type.
I said the term most commonly employed in French: the list of that term's French parasynonyms is very long, reflecting changing fashions and innovations, as this haphazard and not at all exhaustive sample may suggest: introduction, avant-propos, prologue, note, notice, avis, présentation, examen, préambule, avertissement, prélude, discours préliminaire, exorde, avant-dire, proème – and for the postface, après-propos, après-dire, postscriptum, and others. Naturally, many nuances distinguish one term from another, especially when two or more of these texts appear together, as in the didactic type of work, where the preface takes on a function simultaneously more formal and more circumstantial, preceding an introduction that is tied more closely to the subject of the text. This is a distinction Jacques Derrida makes very well apropos of the Hegelian paratext:
The preface must be distinguished from the introduction. They do not have the same function, nor even the same dignity, in Hegel's eyes, even though the problem they raise in their relation to the philosophical corpus of exposition is analogous. […]