All formats below may contain raster data or vector data, or a mix of both.
EPS is effectively obsolete. It offers no transparency or color management support.
Illustrator EPS is different than anyEPS in that it is read back into Illustrator as a native format that does support transparency and color management.
PDF is Adobe’s Portable Document Format, and there are many ways to write a PDF inside and outside of Adobe applications. It was originally designed as a read-only, deployment format.
Illustrator PDF is a specialized dual format that includes PDF data for reading outside of Illustrator and Illustrator-native data for reading back into the application as an AI-equivalent.
While several advancements in vector graphic construct have fostered a misplaced notion that transparency is in play in vector-editing environments, the concept of “transparency” only applies to raster data. EPS can only present the illusion of raster transparency via inclusion of a clipping path.
For the purposes of your professional graphic design output, it should have gone away more than 10 years ago.