While causal diagrams are a specific type of Bayesian network where arrows indicate direct causal relations (or the possibility of one), general Bayesian networks do not require causal relationships. The primary difference lies in the meaning of the arrows:

• Probabilistic Bayesian Networks: Arrows directed into $Y$ mean that the probability of $Y$ is governed by conditional probability tables for $Y$, given observations of its parent variables.
• Causal Bayesian Networks: Conditional probability tables specify the probability of $Y$ given interventions on the parent variables.
• Structural Causal Models: Lacking conditional probability tables, arrows mean $Y$ is a deterministic function of its parents and an exogenous variable $U_Y$: $Y = f_Y(X, A, B, C,…, U_Y)$.

Both probabilistic and causal Bayesian networks specify probabilities for $Y$, not specific values.