I think you might be right, a quote from Friston on the relationship (in reference to belief propagation):
"We turn to the equivalent message passing for continuous variables, which transpires to be predictive coding [...]"
It could be that belief propagation is in the context of discrete variables, whereas predictive coding is in the context of continuous, both of which are a form of (variational) message passing.
"We turn to the equivalent message passing for continuous variables, which transpires to be predictive coding [...]"
It could be that belief propagation is in the context of discrete variables, whereas predictive coding is in the context of continuous, both of which are a form of (variational) message passing.