The abbreviations e.g. and i.e. are both from Latin. Though these abbreviations are used for clarification, they aren't the same. Let's look at how these abbreviations function.
The abbreviation e.g. provides an example. Here's an example: He has many hobbies, e.g., chess, tennis, photography and karate. In contrast, the abbreviation i.e. restates an idea more clearly or gives more information. For example, it happened in April, i.e., three months ago.
In certain cases, the use of e.g. and i.e. can change the meaning of the sentence. If we write "The fish are thriving in the new pond, e.g., the new goldfish," we can infer that there are more fish in the pond than just goldfish.
But if we write "The fish are thriving in the new pond, i.e., the new goldfish," we can infer that the only fish in the pond are the new goldfish. The abbreviation clarifies that the fish in the pond are the new goldfish.
Though e.g. and i.e. are both used for clarification, they serve different functions. The abbreviation e.g. provides an example, but i.e. provides more clarification or information. In fact, the abbreviation i.e. can be replaced with in other words. Though the two abbreviations are similar, they aren't identical.