Difference between EPS and Ai Files.

Around the year 2000 transparancy was introduced in Illustrator.

That introduction made EPS a format of the past.

PostScript (and therefore Encapsulated PostScript (EPS)) does not support transparency and made PDF which supports transparency, the preferred format.

An Illustrator EPS ( encapsulated postscript source ) has the ability to carry all of the document info such as fonts, placed image files, size, and vector elements.  Illustrator ( .ai ) file also encompasses all of the document info and also has the additional benefit of retaining all layers and raster effects as "live" elements that are not flattened in a file such as an EPS.  The advantage to EPS is many RIPs and direct-to-plate machines can enterpret the EPS more efficiently than a live, layered illustrator document.  However, both file formats can be converted to PDF which can then be enterpreted by the RIP or output device driver.  You should study these formats further by getting a copy of Adobe's Print Publishing Guide.