I would say Rust's type system has a lot more in common with Haskell/Ocaml than with C++, at least, although it's not quite as flexible as what Haskell offers (a lack of HKT is painful sometimes).
No typeclasses (and associated goodness), GADTs, HKTs, Monadic IO, first class functions, generic deriving, higher rank types, existential type, etc. These are bread-and-butter features in day-to-day Haskell work. Rust's type system isn't powerful enough to build the vast majority of the tools that Haskell programmers use every day.
I don't mean this as a criticism; The Rust design seems solid. But different priorities lead to different trade-offs, and the end result is a very different type system.
Also, traits objects are existential types, and closures & functions are as first class as they are in Haskell (main difference is a bit more verbosity).