  Nowadays contextuality is the hotest topic of quantum foundations and,
especially, foundations of quantum information theory. This notion is
characterized by the huge diversity of approaches and interpretations. One of
the strongest trends in contextual research is to identify contextuality with
violation of the Bell inequalities. We call this sort of contextuality {\it
Bell test contextuality} (BTC). In this note, we criticize the BTC-approach. It
can be compared with an attempt to identify the complex and theoretically
nontrivial notion of randomness with a test for randomness (or a batch of
tests, as the NIST-test). We advertize {\it Bohr contextuality} -- taking into
account all experimental conditions (context). In the simplest case, the
measurement context of an observable $A$ is reduced to joint measurement with a
compatible observable $B.$ The latter definition was originally considered by
Bell in relation to his inequality. We call it {\it joint measurement
contextuality} (JMC). Although JMC is based on the use of counterfactuals, by
considering it in the general Bohr's framework it is possible to handle JMC on
physical grounds. We suggest (similarly to randomness) to certify JMC in
experimental data with Bell tests, but only certify and not reduce.
