I was a bit apprehensive because rust has like a gazillion different function types but here it seems to work like just any other language with a HM type system.

The fn(T)->R syntax works for functions without associated data, it discards details of the implementation and works like function pointers in C. This allows them to be copy and 'static.

The other function types can have data with them and have more type information at compile time which allows them to be inlined.
These functions each have their own unwritable type that implements the function traits (Fn(T)->R, FnMut(T)->R and FnOnce(T)->R) depending on their enclosed data.

I hope I remembered everything right from this video by Jon Gjengset.