So it sounds like you're using the service communication to mean the stream? Although "toward the original caller" suggests that two inter communicating services would be flip-flopping for ownership of "upstream". Aardvark calls Bear, Aardvark is upstream, Bear calls Aardvark.. Bear is upstream.
Stream could also refer to data (upstream=original/raw, downstream=processed/final), the overall process stage (upstream=prior stage, downstream=next stage - this requires knowledge of the system architecture, the stage boundaries are likely business-defined), some business term (eg in energy upstream=energy producer, downstream=consumer). A stream and the messaging direction may not match.