a real world point of view
A pick-up is a shot or sequence recorded after principal photography has ended. but which could not generally be described as a special effect. It can be created for a number of different reasons. Generally, however, it is a shot called for by the script, but which requires few actors. For instance, the shot of the cat entering the box in Fear Her and Mickey Smith's initial scene in School Reunion were actually pick-ups completed after principal photography involving David Tennant and Billie Piper had wrapped.
Pick-ups may also be new, usually brief, scenes involving the principal actors which are needed to either solidify the meaning of another scene, or merely to make the episode run to the proper length. In Rose, much of the scene of the Ninth Doctor walking back to the TARDIS after initially visiting the Tylers' flat was a pick-up used to make the episode longer, but it also underscored the narrative intent of other scenes.
Re-shoots are closely related to pick-ups, but they imply the actual re-recording of a scene already completed.