CDR was a file format developed by the Corel Corporation and is used primarily for Vector graphic drawings. It is used as the default format from the Corel Draw application which was first developed in 1987 by Michael Bouillon and Pat Beirne who were tasked with developing a vector based illustration program that Corel could package with their desktop publishing solutions. In 2007 Microsoft took exception to the CDR format wrongly blaming it for some security vulnerabilities in it's Microsoft Office suite of products. They concluded that actually this was innacurate and developed a bunch of tools to allow users to import CDR files into MS Office 2003.
There is no publicly available CDR file format specification. It has however evolved over time from it's initial offering in January 1989 to the present day where it is a different beast to what was initially developed to include including support for color management and spot colors, and has a basic support for text.
PDF is a file format developed by Adobe Systems for representing documents in a manner that is separate from the original operating system, application or hardware from where it was originally created. A PDF file can be any length, contain any number of fonts and images and is designed to enable the creation and transfer of printer-ready output.
Each PDF file encapsulates a complete description of a 2D document (and, with the advent of Acrobat 3D, embedded 3D documents) that includes the text, fonts, images and 2D vector graphics that compose the document. They do not encode information that is specific to the application software, hardware, or operating system used to create or view the document.