It is kind of goofy that we use Latin abbreviations for those phrases, isn't it? I think it makes it unnecessarily confusing. The only reason I can keep them straight is I took Latin for three years. If it helps,
i.e. stands for
id est ("that is") and
e.g., which stands for
exempl grti ("for the sake of example").
In German, they abbreviate "that is" as
d.h., which stands for
das heit ("that is" or "that means"). They abbreviate "for example" as
z. B., which stands for
zum Beispiel ("for [the] example). Pretty logical, yes?