WebGPU is a specification for safe, efficient, cross-platform access to the GPU. It is intended to provide a small set of core primitives that are widely implementable without compromising safety or performance: attention is paid to both use from many client platforms (such as Rust, C, JavaScript, and WASM) and to implementation on many graphics backends (not only in terms of Metal / DirectX 11/12 / Vulkan / OpenGL drivers, but also in terms of trying to choose core features that are actually implemented on things like mobile GPUs, which are often left out of powerful modern graphics abstractions).
wgpu-rs is an end-to-end implementation of that spec, for a Rust frontend and many backends. It is designed so that the same code can be used on the web (via WASM) or on native, with no changes to the implementation; however, you can happily ignore the WASM compilation target and just use it natively. It also includes some extensions for widely supported features that aren't available on all GPUs, that you can request if you are willing to restrict the platforms you run on (this is especially helpful on native).
As you can see, the fact that it implements the WebGPU spec is very relevant because it inherits all the nice properties of the spec (efficiency, safety, and portability), as well as because there is a specification that you can refer back to in order to figure out (mostly) what the behavior is supposed to be. There is nothing misleading going on here about saying it's a WebGPU implementation. If there's anything misleading, it's probably the name of the spec (but that ship has long since sailed).
The other two major components of the system are:
* wgpu-core. A cross-platform, safe, efficient, pure-Rust implementation that is used by wgpu-rs, but does not actually implement the full WebGPU spec, and is not really designed for ease of use. It is mostly intended as the basis of other implementations of WebGPU frontends, such as wgpu-rs, wgpu-native (C bindings), and implementations of backends in larger systems like Deno and Servo.
* wgpu-hal. A cross-platform, efficient, unsafe, pure-Rust implementation that primarily exists to abstract away differences between platforms targeted by wgpu-core. The lack of attention to safety means it can often approach or match the performance of the native drivers, but also makes it extremely hard to use, and the exposed API is very closely tied to whatever wgpu-core needs (this is a big difference between it and the older gfx-hal, which was intended to a broader unsafe abstraction layer for independent use).
These two systems are not as cleanly tied to WebGPU, but they are still primarily intended for use by clients that implement the WebGPU spec. That said, this is not a requirement--there are a few other abstractions built directly on top of wgpu-core or wgpu-hal, and they do not consider themselves as WebGPU implementations (because they aren't!).