So both versions are kind of related, but differ in scope (all functions vs. only end-to-end functions), placing (end hosts/in the core vs. higher/lower layers, not talking about what device), and goal (flexibility vs correctness of the system).

The authors of the papers on which this is based never explicitly acknowledge that there are two versions.
Barbara van Schewick says in her book that there being two versions often leads to confusion in, e.g., policy debates.