I thought Stream was just a marketing term for their OpenCL development software.
Stream was their marketing name for gpu computing in general, i think.
AMD definitely had their own language, i can't recall exactly what it was called. I think it came out of Stanford?
Anyway, it was never very popular, which explains why they dropped it completely for OpenCL when that came out. CUDA had way more backing and publicity, so NVidia was a lot more reluctant to stop supporting it.