Isn't 'Cuda a model, not a nickname?

I'm a little fuzzy on the details, but I believe all A body barracudas were, well, barracudas
then at some point when it shifted to the E platform they came out with the 'cuda trim level, which was the high power optioned one
and if I'm not mistaking the next model year (or maybe the one after that) the dropped barracuda all together and called all of them 'cudas