A strip-cut shredder is the most basic kind, which simply cuts paper, cards, and CDs into thin strips. These don’t offer the best level of security since anyone who finds these shredded strips would be able to reassemble the strips to form the completed original with just a bit of patience and glue. They are fast and cheap, and for low stakes, domestic usage is perfectly up to the task. These are also a convenient way to prepare a waste paper for recycling.
A Cross-Cut shredder offers more robust security, usually at a higher cost. Instead of documents just being cut into thin strips, it will also cut each individual strip into multiple smaller pieces. This would significantly increase the work required to reassemble any shredded documents, so these are a good choice for more sensitive personal or business documents.
A Micro-Cut shredder will turn paper into confetti, turning a single sheet of paper into thousands of tiny pieces. This would take an extreme forensic operation, and a lot of time and effort, to even attempt to reassemble. This is ideal for the most sensitive documents that you would want to be absolutely certain have been destroyed, but it does make it the most expensive type of shredder, and it can take quite a long time to fully shred documents.