Diamond cut and confetti cut are both types of crosscut shredders. Diamond cut is a term usually used to describe short crosscut pieces of paper that resemble a diamond. Confetti cut shredded particles are longer and resemble confetti.
Since the paper is cut in regular shapes it can be re-assembled with a scanner and some software. A more secure method is to tear the paper apart by the fiber in irregular shapes. Those are known as a hammermill, "pierce and tear" or grinder.