“I.e.” stands simply for “that is,” which written out fully in Latin is ‘id est’. “I.e.” is used in place of “in other words,” or “it/that is.” It specifies or makes more clear.
“E.g.” means “for example” and comes from the Latin expression exempli gratia, “for the sake of an example,” with the noun exemplum in the genitive (possessive case) to go with gratia in the ablative (prepositional case). “E.g.” is used in expressions similar to “including,” when you are not intending to list everything that is being discussed.
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