  There are two different notions of holonomy in supergeometry, the supergroup
introduced by Galaev and our functorial approach motivated by super Wilson
loops. Either theory comes with its own version of invariance of vectors and
subspaces under holonomy. By our first main result, the Twofold Theorem, these
definitions are equivalent. Our proof is based on the Comparison Theorem, our
second main result, which characterises Galaev's holonomy algebra as an algebra
of coefficients, building on previous results. As an application, we generalise
some of Galaev's results to S-points, utilising the holonomy functor. We
obtain, in particular, a de Rham-Wu decomposition theorem for semi-Riemannian
S-supermanifolds.
