e.g. means "for example" (it stands for the Latin phrase exempli gratia). You should use it before giving an example or a partial list that illustrates your point.
i.e. means "that is" or "that is to say" or even "in other words" (it stands for the Latin phrase id est). You should use it when you want to specify, define or proffer further explanation.
Certain Roman emperors (e.g. Nero) were renowned for their sexual vice.
Nero is one such example, but by using e.g. you are letting the reader know that you might have chosen another name, such as Caligula or Tiberius (or any of them really - they were all perverts).
The Italian Upper House (i.e. the Senate) has the same powers as the Lower House (i.e. the Chamber of Deputies).
In this case, you are not giving an example, you are explaining that the Upper House is the same thing as the Senate and the Lower House the same as the Chamber of Deputies. You are defining the term in another way.
You do not absolutely have to put e.g. or i.e. into italics, but it would be nice if you did.
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