  In general relativity, `causal structure' refers to the partial order on
space-time points (or regions) that encodes time-like relationships. Recently,
quantum information and quantum foundations saw the emergence of a `causality
principle'. In the form used in this paper, which we call `process
terminality', it states that when the output of a process is discarded, then
the process itself may as well be discarded. While causal structure and process
terminality at first seem to be entirely different notions, they become
equivalent when making explicit what the partial order actually encodes, that
is, that an event in the past can influence one in its future, but not
vice-versa. The framework in which we establish this equivalence is that of
process theories. We show how several previous results are instances of this
result and comment on how this framework could provide an ideal, minimal canvas
for crafting theories of quantum gravity.
