These two abbreviations are often confused as they look similar. It's much easier to remember the difference if you know what they mean. Both terms are Latin. E.g. Stands for "exempli gratia" which means "example given" or, as we would say, "for example." You use it instead of giving a full list of things. For instance (or e.g.!) you might write, "You need to take up some sort of exercise, e.g. Aerobics." This indicates that aerobics is just one of several different types of exercise you might recommend. On the other hand, i.e. Stands for "id est" meaning "that is." This term is used to specify exactly what you mean, i.e. To eliminate other examples. If a teacher (Mr Brown) tells a student, "Give the paper to your teacher, i.e. Me," he means: Give it to me, Mr Brown, and no other teacher.
