  We present a comparative study of pair correlations and currents through
superconducting-magnetic hybrid systems with a particular emphasis on the
tunable Bloch domain wall of an exchange spring. This study of the Gor'kov
functions contrasts magnetic systems with domain walls that change at discrete
points in the magnetic region with those that change continuously throughout.
We present results for misaligned homogeneous magnetic multilayers, including
spin valves, for discrete domain walls, as well as exchange springs and helical
domain walls --such as Holmium-- for the continuous case. Introducing a
rotating basis to disentangle the role of singlet and triplet correlations, we
demonstrate that substantial amounts of (so-called short range) singlet
correlations are generated throughout the magnetic system in a continuous
domain wall via the cascade effect. We propose a classification of $0-\pi$
transitions of the Josephson current into three types, according to the
predominant pair correlations symmetries involved in the current. Properties of
exchange springs for an experimental study of the proposed effects are
discussed. The interplay between components of the Gor'kov function that are
parallel and perpendicular to the local magnetization lead to a novel
prediction about their role in a proximity system with a progressively twisting
helix that is experimentally measurable.
