No doubt, terminology can be confusing. I can't remember what a streaming core is, so let me explain it in more general terms.
The HD7970 has 32 cores by any reasonable comparison with CPU cores. Each core is a compute unit. Each core has 1 scalar unit and four vector units. Each vector unit is 16 lanes wide. Each lane of the vector unit is a scalar ALU, and that is described as a "processing element" in OpenCL terminology.
I think we tend to list thousands of "stream cores". What that means is that a "stream core" is a scalar ALU within a vector unit: that is there are 64 of them in each compute unit.
Thanks for the explanation