No. They're not synonyms. They don't mean the same thing.
I agree they're definitely related (internet-radio is likely a subset of streaming) but I don't think they're close enough to warrant just doing away with. If we infer video streaming to be part of streaming, we're also dealing with drastically different technologies and applications.
I'm not saying that things might not need tidying up .streaming as it is might need splitting up into things that actually mean something rather than a word that means different things in different contexts...