I think these are much higher level with larger vectors.

With vectors he means the low level vectors of the CPU.

So if you want to write your own low level algorithms, without going down to the actual intrinsics.

This is a SIMD library (vector in the sense of doing many things at once), what you linked are maths library (vector as in mathematical concept). There’s clearly a bunch of overlap, both are used to do calculations and afaik the libraries you link also use SIMD when they can, so the practical difference is that this library is lower level and more generally applicable (but presumably more complex or difficult to work with).

If you don't actually need higher level math functions or it's prohibitive to implement something at the higher level. For example if you have an operation where you know the sparse-ness(?) of a matrix at compile time but the values of the matrix can change, you may want to implement the matrix multiplications by hand using SIMD ops.