As a US high school student I can try to explain what's taught in the classes for those who are not familiar. Here's how it works at my high school. Algebra>geometry>algebra 2>precalc. From 9-12 grade. Students have the option of taking algebra in 8th to get ahead and taking AP calc senior year.
Disclaimer: i took algebra 2 online during 9th grade to skip it. And took algebra 1 in 8th grade instead of 9th. Currently in 12th so it's been a while since algebra 1. I have often helped my friends work on various assignments so I am sorta familiar with the topics but I may be off in some areas. Also I'm sure it varies by school/city/state.
Basically algebra 1 covers basic algebra. Distributive property, the various forms of linear and quadratic equations. I think they do quadratic formula, not 100% sure though.
Next is geometry. This covers all the geometry rules, and an introduction to proofs was there too I think. Also has basic trigonometry, though not much. Honestly I don't remember much of this class.
Algebra 2 covers logarithms. Matrices and using them to solve systems of equations. Completing the square.... Systems of equations. And more algebra type stuff.
Pre calculus is next and last for most students Covers the rest of trigonometry, and transforming sin waves that kind of thing. Also solving more complicated algebra equations, favoring though synthetic devision, different methods of finding zeros of equations. Also covers rational equations, like the ugly fractions with quadratics on top and bottom. Honestly pre-calc is mostly trigonometry. I think they do limits and the end. With the derivative equation being the very last thing as an intro to calc.
Sorry for the poor explanation. I felt like I would know this as I have friends taking algebra 2 and precal, and my little sister is in algebra 1. But I don't think I know all that's covered, and I'm sure I missed some important stuff.
As far as I know geometry is only in the middle there to show that basic algebra rules can translate to geometry. Things like setting angles equal to each other and doing systems of equations. I know we briefly covered proofs and that was a nice thing doing logic. And we learned all the side-side-angle rules and all that. Showed how math is based on lots of properties and everything derives from those. It has an intro to trigonometry, but that isn't really covered again until precalc- a year after algebra 2. So it's a weird system. Algebra 2 is stuck in the middle of trigonometry stuff, and geometry is shoved in the middle of the algebra. It kinda somehow works though because the topics are all related. Like the geometry problems will all have algebra in them, so you still need to know algebra, things like that.