You can use closures as functions with type inferred signatures

Closures capture variables so have significant differences compared to inner functions. Capture can affect lifetimes so the difference is significant in Rust.

Closures don't have to capture variables. If they don't then they're equivalent to functions.

That's what I thought too, but I fixed some compiler errors by turning a closure into an inner function. Probably a PBKAC, but...

Perhaps it's due to the fact that you can't really have type-generic closures in Rust: once the compiler has inferred one type, the closure cannot be used with another type. In contrast, inner functions can have any number of additional type parameters.