in Netgen, high order curved elements are represented by a hierarchical basis, which is better conditioned in comparison to a Lagrange basis, for high p. It makes it also easy to vary p over the mesh, i.e. straight edges don't need high order basis functions at all.
Beside vertices, coefficients are associated with edges in in 2D/3D, and faces in 3D. No element-interior coefficients are needed.
In general, we don't have the same basis (or even the same space) for the element mapping, and the finite element space, i.e. no isoparametric elements.
For order=2, we get the traditional nodal 6-node trigs / 10-node tets using mesh.SecondOrder().
Maybe you consider to go with mesh.SetDeformation(gridfunction) ?