These are just combinators [1] with long names, right?

[1] https://www.npmjs.com/package/combinators-js

Nope. Example of recursion schemes:

You have a binary tree

    data Tree a = Branch (Tree a) (Tree a) | Leaf a

This is a recursive structure since a Tree can be made up of other Tree's. We can take a slice of the tree:

    data TreeNode a child = Branch child child | Leaf a
    data Fix f = F (f (Fix f))
    type Tree a = Fix (TreeNode a)

    sumTree :: Tree Int -> Int
    sumTree = cata algebra
      where
        algebra (Branch a b) = a + b
        algebra (Leaf a) = a

You might notice that we didn't do any recursion in sumTree because cata captures how to traverse the tree. Catamorphisms are the simplest recursion schemes, there are variants that keep track to our position in relation to the rest of the tree or memoize computations and so on.

I see. You might pass a combinator into a catamorphism, but the morphism itself isn't a combinator?