Yes, functional programming is very similar to OO.

OO:

    class SomeType { 
        <data> ; 
        SomeOtherType function1() { 
            this.whatever ; 
            ... 
        }
    }

FP:

    data SomeType ...
    f1 :: SomeType -> SomeOtherType
    f1 this = whatever this >> ...

Same idea, different syntax. (Type classes will allow polymorphism, if that's what you're after.)

You are thinking of the abstraction in terms of its implementation. There is no reason why a method in a class would physically be in that class; the class just acts as a namespace:

   class Foo { method }
   Foo.method();

and

   (defmethod Foo.method ...)
   (Foo.method)

are the same.