  We study the notion of causal orders for the cases of (classical and quantum)
circuits and spacetime events. We show that every circuit can be immersed into
a classical spacetime, preserving the compatibility between the two causal
structures. Using the process matrix formalism, we analyse the realisations of
the quantum switch using 4 and 3 spacetime events in classical spacetimes with
fixed causal orders, and the realisation of a gravitational switch with only 2
spacetime events that features superpositions of different gravitational field
configurations and their respective causal orders. We show that the current
quantum switch experimental implementations do not feature superpositions of
causal orders between spacetime events, and that these superpositions can only
occur in the context of superposed gravitational fields. We also discuss a
recently introduced operational notion of an event, which does allow for
superpositions of respective causal orders in flat spacetime quantum switch
implementations. We construct two observables that can distinguish between the
quantum switch realisations in classical spacetimes, and gravitational switch
implementations in superposed spacetimes. Finally, we discuss our results in
the light of the modern relational approach to physics.
