Rust doesn't do magical garbage collection.
Rc<T> does reference counting, which is a form of garbage collection, but you get to choose where it gets applied, so it's a linear cost with no magical GC pauses or whatever. Rc isn't unique to Rust, it exists in C++ too.
RefCell makes mutation within an Rc safe. It panics if you misuse it.
http://manishearth.github.io/blog/2015/05/27/wrapper-types-i... has more on the Rc<RefCell<T>> pattern
In academia reference counting generally falls under the umbrella of GC. In the industry "GC" usually means "tracing GC".
The terminology is irrelevant to the point I'm making. I did make a distinction between RC and the "regular magical kind" of GC.
From a 1976 paper on automatic memory management https://www.cs.purdue.edu/homes/hosking/690M/deutsch.pdf
"Automatic reclamation of storage no longer in use is done by the following two techniques:
* Garbage collection * Reference counting"
Note that these are two separate items and that one is not a subset of the other (and vice versa). It is simply incorrect to call reference counting "garbage collection" when the academic and industrial practices already have explicit meanings to these two terms.
I'm not saying the term always is used that way in academia. I'm saying that it's sometimes used that way, and that it's valid to call RC a form of GC.
Ironically I said that RC was a form of GC to avoid precisely this argument, because if I say "Rust doesn't have GC" I'll have a bunch of folks telling me that RC is a form of GC. This is largely irrelevant to the point I was making, which explicitly distinguished between RC and tracing ("magic") GC -- which I suspected (but wasn't sure) was what was being asked about.