Short answers, pulled from the story.
A film score is original music written specifically to accompany a film, consisting of timed pieces called cues designed to enhance dramatic and emotional impact. A soundtrack is a broader term that includes both the score and any pre-existing songs used in the film; pop or rock songs dropped into scenes are not considered part of the score.
Spotting is the process in which the director and composer watch a rough cut of the film together and identify which scenes require original music, where each cue begins and ends, and which specific moments on screen need to coincide with musical events. Composers take precise timing notes during spotting to determine the exact length of every cue.
Erik Satie is widely credited with composing the first frame-by-frame synchronous film score, written for director Rene Clair's avant-garde short Entr'acte in 1924. Satie took precise timings for each sequence and built a flexible score of brief motifs that could be repeated and varied in tempo to accommodate inconsistent projection speeds.
A leitmotif is a recurring musical idea tied to a character, place, or concept that returns throughout the score to carry emotional meaning. John Williams used leitmotifs for individual characters including Darth Vader, Luke Skywalker, and Princess Leia in the Star Wars saga; Howard Shore used them for characters and locations in the Lord of the Rings films; and Jerry Goldsmith's Klingon theme from Star Trek: The Motion Picture in 1979 was quoted by later composers in the franchise.
Kubrick chose existing classical recordings, including pieces by composer Gyorgy Ligeti, over the original commissioned score by Alex North, even though he had also hired Frank Cordell to compose for the film. The film became one of the most discussed cases of a director replacing a composed score with temp music.
The Society for the Preservation of Film Music is a non-profit organization formed in 1983 to protect the physical byproducts of film score creation, including written manuscripts, studio recordings, and documents that movie studios had sometimes discarded. Preserving the written music is essential for performing scores in concert and producing new recordings.