
Some journalists called those objects "flying saucers" and the term stuck. Large numbers of other people saw them, and half a year later, Captain Thomas Mantell died chasing one of them. Believers came to the conclusion that they were extraterrestrial spacecraft, while skeptics had a variety of other theories for the sightings: planets and stars, balloons, aircraft, meteors, ... and outright fakery.
The US Air Force started investigating flying saucers on the ground that some of them might be secret Russian airplanes and spy balloons. They first did so in secret, and word leaked out that some USAF investigators thought that the saucers were extraterrestrial spacecraft. This led some people to believe that the USAF was covering up what it knows about these odd entities, and coverup theories have been a staple of UFOlogy ever since.
Around 1952, the USAF introduced the term "unidentified flying object" or "UFO" for these entities, and flying-saucer believers gradually shifted to using "UFO".
I myself have seen one, a bright fuzzy whitish object above some clouds from an airplane. It stayed in place as the plane moved, and on one occasion, it dimmed and got brighter after that. I discovered later that I'd likely seen a subsun, a reflection of the Sun sometimes seen above ice-crystal clouds.