Not really, they both mean the same thing and they are both Latin abreviations
i.e. stands for “id est”, that can be transated : “that is”. It is generally used in scientific publication when submitting an exemple to corroborate a statement.
e.g. stads for “exempli gratia” and may be translated : in a way of example or, more simply: “for example”.
You may have noticed the logo of Metro Gold Mayer (the cinema production house) at the beginning of all their films. It is a lion head roaring from the middle of a circle. On that circle is written : “Ars gratia artis” which means “The Art for the Art”. An ambitious enagement for Metro Gold Mayer, and a good example of the proper usage of the word “gratia”.