Husserl: Presentation (Gegenwärtigung), Re-presentation (Vergegenwärtigung)

Presentation (Gegenwärtigung):

Husserl uses the term Gegenwärtigung to designate the subset of presentations (Vorstellungen) that present an object originally, that is, intuitively. Such a presentation intuitively presents (gegenwärtigt) an object by virtue of the fact that it comprises filled intentional moments originally and directly presenting (gegenwärtigend) a side or aspect of an object. Other moments in the act make present or re-present (vergegenwärtigt) those sides and aspects of the object that are not originally and directly present. Hence, while the concrete act or presentation directly and originally presents its concrete object, not every moment within the act originally makes present its correlate, that is, the side or aspect of the object to which it is directed.

Re-Presentation, Presentification or "making present"(Vergegenwärtigung):

Husserl uses the term Vergegenwärtigung to designate a presentation (Vorstellung) that does not present an object originally, that is, as intuitively present. Such a presentation makes present (vergegenwärtigt) an absent object in an empty intention (or only partially fulfilling intention) either by representing the object, that is, presenting it again as in memory, or by emptily expressing a sense in expression, or by crafting an image, or in expectation or wishing or hoping, and so forth. All of these kinds of experience are contrasted with perception (Perzeption, Wahrnehmung) and other intuitive acts.

Source: see the excellent John Drummond's Historical Dictionary of Husserl’s Philosophy.