There are essentially two main types of paper shredders for home and medium-volume business use, based on how the machine does its job: strip-cutting and cross-cutting.
A cross-cut (or confetti cut, or particle cut) shredder is the more sophisticated, or complex, of the two. There are two sets of blades or drums rather than just a single blade, and these blades operate at an angle to one another. As they "chew" the paper, they alternate the direction of the cut from vertical to horizontal, so the paper is broken down like confetti rather than strips or "spaghetti cuts." The paper may end up as rectangles, diamonds, or parallelograms. If the cross-cutter results in pieces or "chad" as small as 3 mm x 9 mm, it is generally referred to as a micro-cut shredder. (Even more advanced and secure are disintegrator, granulator, hammermill, and grinder methods.)
Since cross-cutting is a process that requires more advanced machinery and cuts that result in smaller, rougher paper pieces, cross-cut shredders are generally more expensive. Another down side is that these types of machine are more likely to require maintenance or repairs.
Businesses and individuals that are especially concerned about privacy and security (such as those bound by laws such as FACTA and HIPAA) usually opt for a cross-cut shredder, or a micro cut shredder. It's theoretically possible for an ambitious thief or snoop to piece together strips cut from a strip-cut shredder, reassembling the printed information into readable form. But even the most painstaking bad guy would find it much harder, if not impossible, to make sense of papers that have gone through a quality cross-cut shredder. A bit of history: Oliver North used a cross-cut shredder to destroy Iran-Contra documents in the mid-1980s.
Companies that manufacture cross-cut shredders include: Fellowes, Royal, Aurora, Black & Decker, GBC, and Dahle. Cross-cut or confetti shredders come in both desktop models and floor models.