What are typeclasses if not inheritance? As someone without a formal CS background, a type with multiple typeclasses sure looks to me like a class inheriting from multiple interfaces.
Overloading not inheritance. It is closer to the notion of interfaces in traditional OO languages, but it's a mistake to confuse interface implementation as inheritance.
This is a common problem with traditional OO languages: they conflate inheritance with subtyping, ie. "Y inherits the behaviour of X" is not always the same as "Y can be used anywhere an X can be used" (subtyping). C++ has "private inheritance" to separate these notions now, but it's a kludge from this initial design mistake.
So type classes use subtyping, but not inheritance. Interface implementation is also closer to subtyping than inheritance.
When you separate data from functionality into separate "things", composing things out of them becomes nicer.
I'm not a Haskell programmer, but AFAIK type classes contain functionality, NOT data (state).
Example of what I'm talking about: Clojure's Protocols.