What is the difference between deterministic and confluent?
If a binary relation is confluent and terminating, then the map from initial state to final state is total and deterministic.  The converse also holds.
If a binary relation is confluent, the binary relation need not be a function.
You'll have to decide what you mean by &quot;deterministic&quot; and whether you refer to what the original state ultimately leads to (then the answer to your question is yes, as mentioned in the first paragraph of this answer) or whether you refer to the behavior in a single step of the system (then the answer is no, as mentioned in the second paragraph of this answer).