The Rust Programming Language, first edition says that Rust does not have a garbage collector:
It maintains these goals without having a garbage colle
This article is a bit old, regarding how Rust has changed now, but it highlights what it means that Rust does not have GC. Only RAII and ownership are intrinsic to Rust. They helps writing reference-counting alike GCs such as Rc and Arc, but those are not part of the language, they're part of the standard library. And it makes a huge difference.
If you consider writing an operating system in Rust, you can't use any form of GC in part of your code or use the standard library. At this level, it's important to know what is part of the language and what is not. For a simple example, have look here.
In contrast, in a language such as Java or Python, you can't prevent your code from using the GC as it use it implicitly by design of the language.
In Rust, like in C/C++ a GC is part from a library and it's use is explicit.