  Curry-Howard correspondences between Linear Logic (LL) and session types
provide a firm foundation for concurrent processes. As the correspondences hold
for intuitionistic and classic versions of LL (ILL and CLL), we obtain two
different families of type systems for concurrency. An open question remains:
how do these two families exactly relate to each other? Based upon a
translation from CLL to ILL due to Laurent (2018), we provide two complementary
answers, in the form of full abstraction results based on a typed observational
equivalence due to Atkey (2017). Our results elucidate hitherto missing formal
links between seemingly related yet different type systems for concurrency.
