As defined in "The Book of Why", causal diagrams are Bayesian networks where every arrow indicates either a direct causal relation or the possibility of a direct causal relation in the direction that the arrow is facing. Unlike causal diagrams, Bayesian networks do not have to be based on causal relations.

The meaning of the arrows is a major difference between Bayesian networks and causal diagrams.

In a probabilistic Bayesian network, the arrows into $Y$ mean that the probability of Y is governed by the conditional probability tables for $Y$, given observations of its parent variables. The same is true for causal Bayesian networks, except that the conditional probability tables specify the probability of $Y$ given interventions on the parent variables. Both models specify probabilities for $Y$, not a specific value of $Y$.

In a structural causal model, there are no conditional probability tables. The arrows simply mean $Y$ is a function of its parents, as well as the exogenous variable $U_Y$: $Y = f_Y(X, A, B, C,…, U_Y)$