I've not seen Origins, but this has been inconsistently displayed through the comics.
I believe that, in the most recent canon I've read, Wolverine's claws are bone, laced with Adamantium like the rest of his skeleton. This makes sense (in the comic book usage of the term, at least) because if the claws weren't part of his original skeleton he wouldn't have had the musculature in place to extend or retract them.
As for the appearance in Origins, I can't answer why they would appear rough. I would expect that any claws would be similar to a cat's - smooth on the sides. They wouldn't be curved, of course, as they have to be stored in the forearm while retracted. It's likely that the Adamantium bonding would fill and smooth out any irregularities as it plated the bones, which could account for the visual difference you point out.