My understanding is that hacspec is the language (a subset of rust), and hax is the tool that compiles it into format proof languages like Coq. Some explanation of the name changes here: https://hacspec.org/blog/posts/hax-v0-1/
> A group of us started hacspec (high assurance crypto specifications), a language for specifying cryptographic primitives as the basis for formal verification, in early 2018 at the HACS workshop. After two iterations on hacspec the project outgrew the name and the initial crypto-oriented scope.
> Here comes hax. hax is a tool for high assurance translations that translates a large-ish subset of safe Rust into the formal languages accepted by proof assistants such as F* or Coq. Backends for other provers like EasyCrypt are under construction.
> A group of us started hacspec (high assurance crypto specifications), a language for specifying cryptographic primitives as the basis for formal verification, in early 2018 at the HACS workshop. After two iterations on hacspec the project outgrew the name and the initial crypto-oriented scope.
> Here comes hax. hax is a tool for high assurance translations that translates a large-ish subset of safe Rust into the formal languages accepted by proof assistants such as F* or Coq. Backends for other provers like EasyCrypt are under construction.