  We study the differences and equivalences between the non-perturbative
description of the evolution of cosmic structure furnished by the Szekeres dust
models (a non-spherical exact solution of Einstein's equations) and the
dynamics of Cosmological Perturbation Theory (CPT) for dust sources in a
$\Lambda$CDM background. We show how the dynamics of Szekeres models can be
described by evolution equations given in terms of "exact fluctuations" that
identically reduce (at all orders) to evolution equations of CPT in the
comoving isochronous gauge. We explicitly show how Szekeres linearised exact
fluctuations are specific (deterministic) realisations of standard linear
perturbations of CPT given as random fields but, as opposed to the latter
perturbations, they can be evolved exactly into the full non-linear regime. We
prove two important results: (i) the conservation of the curvature perturbation
(at all scales) also holds for the appropriate approximation of the exact
Szekeres fluctuations in a $\Lambda$CDM background, and (ii) the different
collapse morphologies of Szekeres models yields, at nonlinear order, different
functional forms for the growth factor that follows from the study of redshift
space distortions. The metric based potentials used in linear CPT are computed
in terms of the parameters of the linearised Szekeres models, thus allowing us
to relate our results to linear CPT results in other gauges. We believe that
these results provide a solid starting stage to examine the role of
non-perturbative General Relativity in current cosmological research.
