It's always been very ambiguous in practice. To avoid ambiguity I usually use `flop/s` but not everyone likes that :)
I couldn't confirm the DR SVD part, but the PROF SVD story appears to be real: https://www.mathworks.com/company/newsletters/articles/profe...
Flop/s makes no sense and is outright wrong. The whole point of flops is to express how many floating point operations are required by an algorithm. How many operations are performed per second is a property of the hardware you're using to run an implementation of the algorithm.
You want to express computational complexity in terms of floating point operations.