We know that books printed digitally have tended to be, like the old stitch about newspapers, black and white and read all over. For most of digital printing's existence, producing professional four-color books just wasn't possible; you had to use offset. But the times they are a-changing, and technological advances are making the production of full-color books in longer short runs more feasible and economical than ever before. The advent of sheetfed digital printing brought us the ability to print full-color books in very short runs—it was responsible for opening up the high-growth photo book market. Now "4-up" and roll-fed "printer/presses" are further changing the full-color publishing paradigm.
Before we go further, let's define some terms, as printers are, in essence, quite different from presses. Printers regenerate the impression for each copy from a digital file, which allows them to use electronic collation and print the pages of a book block in order. Presses, on the other hand, use a physical image carrier (a plate) to reproduce large printed sheets which are folded into signatures, gathered and bound. But printers become, in essence, presses when either the sheet size or output speed starts to approach the specs of an analog reproduction device (aka a press). A "printer/press" is my term for printers that have many characteristics of a press.