How ufl.nabla_grad works?

[dokken]

See for instance the old Q&A. To summarize:
No difference for scalars.

For vectors:

(grad v)_ij = dv_i / dx_j
(nabla_grad v)_ij = dv_j / dx_i

For matrices:

(div v)_i = dv_ij / dx_j
(nabla_div v)_j = dv_ij / dx_i