ib hl has a few more topics, calc bc is just more in depth. ib sl is around precalc or precalc honors level
IB Math HL 1 covers BC calculus, HL 2 covers beyond that and Further HL is even beyond that
Math studies is easy and only vaguely introduces calculus concepts but includes a LOT of useful applied math for people aiming for humanities and social sciences. It’s actually a great course for people who don’t like math because it shows there’s math everywhere in the world. It’s extremely well conceived in relation to its aims.
Math SL over two years covers precalculus and calc AB plus statistics&probability.
Math SL used as a pre-req for HL is a different animal, faster paced.
Math SL is meant for future business majors, premeds, econ majors, stusents who’ll typically need 1-2 semesters of math (typically calc1+ stats)
Math HL is meant for future engineering and math majors. It goes beyond calculus BC (at some schools calc BC and stats are a pre-req for HL2) and includes more types of math. It is extremely difficult, and taken only by very strong students.
Further Math HL is clearly designed for students who are uncommonly advanced at math (prodigies, Aime qualifiers, kids who do AoPS for fun) and there’s even a warning about it in the teachers’ handbook.
This is the typical sequence for my brother’s sequence.
6th Grade - Algebra 1
7th Grade - Geometry
8th Grade - Algebra 2
9th Grade - Pre-IB Precalculus
10th Grade - BC Calculus (University-Level)
11th Grade - IB Further Math HL
12th Grade - IB Further Math HL