wgpu is the name of the Rust library, but it pretty closely follows the WebGPU spec, which you can easily use from C or C++ via Google's `dawn` library. It provides C bindings as well as a templatized C++ API.
Webgpu.h is, AIUI, part of the webgpu spec. Both Dawn (Google’s C++ implementation used in Chrome) and wgpu (Mozilla’s implementation used in Firefox) can be used as concrete implementation of those headers.