Rust's traits are basically Haskell typeclasses, with a few extensions enabled, like multiple parameters.
Trait objects are basically existential types, with a few more restrictions on them. But in essence polymorphism in Haskell and Rust are very similar.
The big thing Rust is missing is higher kinded polymorphism, ie the ability to abstract over type constructors. This makes it easy, for example, to abstract over a container type while putting different things in that container.
This has get approved in the Associated Type Constructors RFC, but it's still in the works for actually landing.
In Haskell you have to supply the entire instance, versus just specializing one method as you can do in Rust. Also in Haskell this extension is not recommended for general use and you won’t often find specialization like this in the wild.
The typical way to do multiple instances for a given type is with trivial newtype wrappers for each instance. See the "Sum" and "Product" monoid instances (although these wrappers are also necessary for instance decidability). This is fine "in the wild."
Also, I'm not sure why you would ever want a "partial instance," as it would mean that your program could be unsafe but still typecheck (I haven't checked out Rust's implementation or motivation). Just use more specific classes, and you can even use a "generic" "instances of the components imply an instance of the whole" class and instance.
When you specialize an instance in Rust, by definition it already has a valid instance that covers that type. So implementing a single method is fine - the other ones are provided by the instance you are specializing.
Newtypes also exist in Rust but this is an alternative that is not the same as the overlapping instances extension.
Trait objects are basically existential types, with a few more restrictions on them. But in essence polymorphism in Haskell and Rust are very similar.
The big thing Rust is missing is higher kinded polymorphism, ie the ability to abstract over type constructors. This makes it easy, for example, to abstract over a container type while putting different things in that container.
This has get approved in the Associated Type Constructors RFC, but it's still in the works for actually landing.