  Nonlocality and contextuality are at the root of conceptual puzzles in
quantum mechanics, and are key resources for quantum advantage in
information-processing tasks. Bell nonlocality is best understood as the
incompatibility between quantum correlations and the classical theory of
causality, applied to relativistic causal structure. Contextuality, on the
other hand, is on a more controversial foundation. In this work, I provide a
common conceptual ground between nonlocality and contextuality as violations of
classical causality. First, I show that Bell inequalities can be derived solely
from the assumptions of no-signalling and no-fine-tuning of the causal model.
This removes two extra assumptions from a recent result from Wood and Spekkens,
and remarkably, does not require any assumption related to independence of
measurement settings -- unlike all other derivations of Bell inequalities. I
then introduce a formalism to represent contextuality scenarios within causal
models and show that all classical causal models for violations of a
Kochen-Specker inequality require fine-tuning. Thus the quantum violation of
classical causality goes beyond the case of space-like separated systems, and
manifests already in scenarios involving single systems.
