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.
Adobe Illustrator Artwork was developed by Adobe Systems for single page vector based drawings in either EPS or PDF formats. The AI format is a strictly limited simplified subset of the EPS format. It is the standard format used when saving out Adobe Illustrator files.
Earlier versions of the AI format are restricted syntax that conform to DSC's Open Structuring Conventions. It was originally a native format called PGF. In order to make PDF files compatible can be achieved by embedding the PGF data within the saved PDF file. This same technique is used when saving EPS compatible files in recent versions of Illustrator.