(Cas)efix denotes a very slight modification of Efix, where parseElanRule(l => r if g = d) is just replaced by the Casfix ATerm parseCaslEq(l = r if g = d). Therefore, (Cas)efix is mainly an Efix ATerm containing some Casfix subterms related to unconditional axioms (of the form strong-equation) and conditional ones (of the form implication). CASL terms are fully parsed in a (Cas)efix ATerm, while ELAN terms are not (yet) fully parsed in a Efix ATerm.
We use (Cas)efix as an intermediate format between Casfix, the CASL abstract syntax, and REF, the ELAN executable format.