The important distinction, then, is obligate garbage collection. Can I write a substantial program that does, and needs, no garbage collection of any kind? In C++ and Rust, yes, trivially, every day.

The distinction matters because without obligate GC, you get the benefit of destructors (or in Rust, the Drop trait), and have the tool for resource management of every kind, usually written "}". Reference counting GC is rarely used in well-designed C++ and Rust programs, simply because there is rarely any need for it. Reliance on shared_ptr or ARC is recognized as a disease of forced Java converts.