We usually call people who live on the Mars "the Martian." Then how do we say people living on the earth? Is "Earthman" acceptable?
"Earthman" sounds like something an alien might say in a science fiction movie or story - it also sounds a little fashioned because it is not gender-neutral (because it includes the word "man").
"Earthling" is similar in feel, but gender-neutral, so it is a better choice in my opinion.
"Terran" is an adjective meaning "from Earth" so some writers use "Terrans" to mean people from Earth.