Most people learn differential equations after calculus 2, alongside calculus 3. It's basically an application of linear algebra techniques to derivatives. Differential Equations is very different from the rest.
Multivariable calculus is what some universities call Calculus 3, so I would imagine they're the roughly same (though again, I haven't checked the catalog for it). Example 2: Using logarithmic functions of Algebra 2. Calculus 3 is basically calculus 2 but with more variables. Khan Academy is your one-stop-shop for practice from arithmetic to calculus.
Calculus 2 expands on integrals, then progresses into infinite sums, and then gets into polar coordinates. Calculus 1 is a course that goes over limits, continuity, derivatives, and integrals. While I haven't checked their specific catalog, you can expect AP calculus AB to have the same material as calculus 1 and expect AP calculus BC to have the same material as calculus 1 and 2. AB only provides credit for calculus 1 and BC provides credit for calculus 1 and 2. AP Calculus AB and BC are both classes for high school students trying to get college credit for calculus.
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