PDF417 is a high-density symbology. It is basically a set of smaller bar-codes. They are great for encoding a large amount of data.
Data Matrix has a high-density storage capacity (it can store up to 2000 characters) and is commonly used to label small items, mostly small electronic components, such as circuit boards.
QR codes are 2D codes mostly used in marketing – in magazine articles, billboards, etc. A phone with the right software for decoding QR codes scans the QR code image, which redirects the phone’s browser to a URL with the information on the image coded in the QR. These codes are becoming increasingly popular, especially among the younger population.