I.e. versus e.g., my teachers use both when she/he is giving us examples, what is the difference? or is there no difference at all?

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”.