Yep, stroking is just filling of the space between offset curves (aka. parallel curves), and that "slightly scaled down version of the first" is the "calculate an offset curve explicitly" approach I mentioned.

Though it is very unpractical because the offset curve of a cubic bezier curve is not a cubic bezier curve anymore, instead it is an analytic curve of degree 10. Thus, in practice the offset curves for stroking are either approximated by polygons or implicitly sampled from signed distance fields.

Raph Levien has a good blog post about it:

https://raphlinus.github.io/curves/2022/09/09/parallel-bezie...

One more thing: Offset curves are different form classical scaling from a center point in all but the most trivial cases where there exists such a center; namely regular polygons. And cubic bezier curves can be concave, even have a self intersecting loop or form a cusp.