The languages are completely different, have different goals, have different design philosophies and exist in distinct eco systems.
All "similarities" are just rust borrowing a few concepts from functional programming languages and has an integrated tool chain like dotnet has. That is literally it.
Rust is a systems level programming language which aims to provide strong compile time guarantees about memory safety, F# is a functional programming language, which aims to bring that style of programming to .NET. These are totally different categories and claiming that F# does what rust does in the .NET ecosystem is plainly false.