In this page there are calculations of variation of Einstein-Hilbert action.
I see variations of terms like this:
$\delta {R^{\rho }}_{{\sigma \mu \nu }}$
where the term is not a functional, and
$\frac {\delta {\mathcal {L}}_{{\mathrm {M}}}}{\delta g^{{\mu \nu }}}$
where we have a functional derivative of a term that is not also a functional.
What is the exact meaning of those expressions?