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.
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.