(covers information from several alternate timelines)
Extraterrestrial was a general term of Latin origins, meaning "outside Earth", where the term "terrestrial" was often described of things said to have originated on Earth. The term was commonly used by Humans during the 20th and 21st centuries to describe alien life and outer space. The term was occasionally used interchangeably with the terms Martian or E.T..
In an alternate 1944 created during the Temporal War, Sal, upon observing the alien Ghrath, he asked Jonathan Archer what that was. Archer, attempting to not reveal too many details, simply told him it was an extraterrestrial, and when asked by Sal if it was a Martian, Archer explained that he didn't know what planet he was from. (ENT: "Storm Front")
Upon landing on Earth in 1986 with the HMS Bounty, Admiral James T. Kirk briefed his crew, stating that he wanted them to be careful because there were in terra incognita. He added, directing his comment towards Spock, that "It's a foregone conclusion [no 20th century Humans] have seen an extraterrestrial before," prompting Spock to cover his Vulcan ears. Star Trek IV: The Voyage Home)
By 1996, the Griffith Observatory, participated in the SETI program, whereas it employed individuals such as Rain Robinson to "watch the skies [...] for signs of extraterrestrial life." Later, she utilized the SETI greeting as its standard greeting designed for extraterrestrials, which was received by the USS Voyager, after the ship had time travelled back to Earth and was later detected in orbit that year. (VOY: "Future's End")
When William Riker and Deanna Troi attempted to explain to Zephram Cochrane that he must launch the Phoenix, Riker stated that an alien ship was about to pass through the Sol system. Cochrane, who was already spooked by the presence of the Borg, was hung up on the word alien, by clarifying, "Alien? You mean extraterrestrials. More bad guys?" (Star Trek: First Contact)
When the distress beacon from the SS Mariposa, which was originally used by Earth's European Hegemony, was being investigated by the crew of the USS Enterprise-D, it had already been confirmed that the code had never been used by any "extraterrestrial source". (TNG: "Up The Long Ladder")
The Enterprise-D was recalled to Sector 001 on Stardate 45959.1 with the understanding that, according to Jean-Luc Picard, "evidence has been discovered indicating the presence of extraterrestrials on Earth five centuries ago." When Picard later inquired what it was that made excavation crew in San Francisco to think that extraterrestrials were related to the discoveries of numerous artifacts, including Data's head, he was informed that the composition of the rock face in the cavern had been altered by exposure to triolic waves; something that would not be found on Earth, even during the 24th century. (TNG: "Time's Arrow")