I got y'all...but y'all not gonna like the answer...
Wolverine's claws rest in his forearms when they are not extended. Originally, they were triggered by a tendon that activated when he moved his wrist. As time went on, he was able to trigger the tendon by thought alone. The claws are actually about 16 inches long, with 12 inches (a foot) protruding out as his famous claws. They came out from the top of his hand, through adamantium shafts & ports connected to his knuckles & forearm bones.
Now, when Magneto ripped the adamantium out of Wolverine, he began to mutate again due to his healing factor having no limitations. This is the famous time when he lost his nose & we found out that he has a bone claws & a whole lot of other mutant abilities (his heightened senses, speed & agility were all seen before as products of his training in Weapon X, not a result of his mutant powers). The bone claws followed the path of the shafts & bushings that were there previously, but the bone claws had two major differences. One is that they were curved, the second is that they wasn't as strong as the adamantium ones, being broken a number of times.
The movies came out & to make it easier, they protrayed Wolverine having the claws coming out in between his knuckles. In real life, this makes no sense, due to the fact that there are major nerves, blood vessels & muscles that control the entire spectrum of your hand usage. A sharp blade slicing through your muscles before healing around the same sharp blade sounds ridiculous.
However, by the 2000's, Wolvie got his adamantium back, lost it & got it back again & to follow the movies, his claws come out from his knuckles now.
They never explained why this was but I have a theory. I think that Wolverine's claws were a secondary mutation & that they were never supposed to come out. However, once Weapon X got a hold of him & coated the claws, the shaft & bushings were a way to make the claws come out instead of being dormant in his forearms, as his body wouldn't have him cut through his own muscloskeletal system. Also, if you were not aware, Wolverine actually "pops" through his skin every time he pops his claws. Every time.
However, when he lost the metal, I theorize that the bone claws, being used by Wolverine the same as the metal ones, basically"regrooved" themselves in their original pathway, through his knuckles. When he got the adamantium restored, they just recoated the claws & did not add the shafts of bushings. Evidence of this is how, in both the movies & comics, when he pops his claws, he bleeds profusely for a minute or so from where the claws come out.
So the answer is both.