If you have a specified causal system you could represent it either way, yes.
Speculating on another reason he may have made the distinction: often he posed problems with specified causal graphs but unspecified functions. So he may have meant that in the problems like these, with one approach you can easily specify some node values as being deterministic functions of other node values, whereas with the other approach you don't (since a specified graph rules out further random influences in one approach but not the other).
Michael Nielsen has posted a long essay explaining his understanding of the Pearlean causal DAG model. I don't understand more than half, but that's much more than I got out of a few other papers. Strongly recommended for anyone interested in the topic.