High School mathematics has changed in many ways over the years, but the basic framework is still largely the same throughout the United States. There are three years of "core" mathematics courses which must be completed to graduate high school. Many states separately require students to take three year-long "math" courses during their high school career, even if they take some of the core classes in middle school. 

Generally, schools organize the core courses by content area (Algebra 1, Geometry, Algebra 2). There is also a growing trend to "integrate" the material so that the first year is an introduction to all of the topics, the second year develops intermediate topics, and the third year completes the final pieces of each topic*. 

Students who are interested in STEM fields would then take Pre-Calculus their senior year to cover some more advanced topics  (especially within Trigonometry) which are necessary for success in Calculus. Starting in the 1980s colleges started to see more and more students take Calculus in high school, and by the 2000s this was an unofficial requirement for students in STEM fields and seen as an advantage for all other students. 

Traditional Path: Start core courses in 9th Grade, option to take Precalculus senior year.

College Prep Path: Start core courses in 8th Grade, take Precalculus junior year, and option to take Calculus senior year.

Accelerated Path: Any path that gets students to Calculus before their senior year. This is most commonly done by starting core classes in 7th grade or double up on core classes.

*The third year of a strong integrated curriculum closely resembles Precalculus. My experience in New York State in the early 2000s was that Precalculus was just a review of Course III and only two "new" topics were discussed (interval notation, matrices). New York stopped offering Course III in the early 2000s and the need to take a separate Precalculus is now more important than it once was.