  We show that out-of-time-order correlators (OTOCs) constitute a probe for
Local-Operator Entanglement (LOE). There is strong evidence that a volumetric
growth of LOE is a faithful dynamical indicator of quantum chaos, while OTOC
decay corresponds to operator scrambling, often conflated with chaos. We show
that rapid OTOC decay is a necessary but not sufficient condition for linear
(chaotic) growth of the LOE entropy. We analytically support our results
through wide classes of local-circuit models of many-body dynamics, including
both integrable and non-integrable dual-unitary circuits. We show sufficient
conditions under which local dynamics leads to an equivalence of scrambling and
chaos.
