You can twist words and say that shared_ptr means C++ has 'garbage collection' but I doubt anyone would agree with you if were were to word it like:
"C++ has a garbage collector"
Ref counting is a form of 'garbage collection' in so far as it is a way to release memory, that's about it. I certainly wouldn't consider Rust's Arc<T> a 'opt in garbage collector'.
In contrast, C's automatic storage duration for stack-allocated items ( http://en.cppreference.com/w/cpp/language/storage_duration#S... ) and Rust's system of ownership for heap-allocated items are things that I'd consider "static lifetime determination".
The term has been used that way since I first heard it back in the '80s, so it's probably not a battle worth fighting at this point.
Yes, of course, there's a formal sense under which reference counting is just an outlying position within the broader world of garbage collection, but from an engineering point of view, it's a significantly different set of tradeoffs, and reference counting doesn't really qualify as the same thing when you're deciding how to structure your program.
Wikipedia lists both tracing and reference counting as forms of GC... hell, when interviewing at Microsoft I was asked to describe the two primary families of GC, expecting tracing and ref counting.
Terminology is useful right up until it isn't. Resting on definitions rather than seeking proper descriptions is a great way to fail spectacularly.
Not a random dude on Internet.
If you're right, you're just some guy referencing an authority. Yay you. If you're wrong, you're totally ... all over the point of what someone else is saying. Instead of trying to force us to see how you're right, why not try to see how someone else isn't wrong?
The papers of computer science, written since the field exists, speak for themselves. One just has to read them.