Calculus is taught in high school. However, it is not mandatory/standard - you have to be on the college track, and it is skippable. (these are all general statements, different school districts make different choices).
For example, in my high school, in a fairly small rural school, we were taught calculus in senior year. I was bored, and did it sooner, but that was the general rule. We also had things like advanced placement biology, physics, and so on. Generally speaking, at the end of those courses you can take the optional AP tests, which allow you to skip the Physics I, Calc I&II, etc., that are the normal fare for freshmen.
I can't recall anyone who had diff eq taught in high school, though we really did end up using it anyway in advanced physics. To roughly sketch the limits of what we did, I remember needing Green's theorem, and having to prove things using elliptic integrals, but nothing much beyond that.
Interesting. When I came to college here in the US (CS, engineering department), I was rather shocked that most, if not all, engineering students came in with zero calculus or advanced physics.
In my school and country, we take calculus 1 & 2 in grade 11; that's two years before we go to college. In grade 12, we take differential equations.