what? off course he can regenerate, as a matter of fact it is believed that it was his regenerative capabilities that enables him to heal rapidly, the ability to heal/replace lost and damaged tissues on a molecular level at an accelerated speed is considered to be very much regenerative.
and yes he can pretty much replace a lost arm or limb, why it makes sense is because if your body can replace lost organs, say heart, lungs, eye, stomach which are tissues etc, it is pretty much easier to grow back a lost arm, the only difference is that it would be slower to replace because of calcium phosphate that makes up the bone/cartilage/tendon tissues. my point is clear, it doesn't make sense if you can heal rapidly but cannot regenerate a lost arm because in order to be able to heal extremely fast like wolverine's healing factor, you need to be able to regenerate those tissues you lost.
the buttom line is that wolverine can die say, there are many ways one can kill wolverine, the easiest way to kill him is if you can shut down his healing factor, throwing him into a volcano, drowing him, cutting his head off, and if you can make him lose a lot of blood then he is more likely to die.
you can't cut off his arm, well his metal one, when his metal skeloton was out, I still think he can regenerate limbs, with the metal skeleton you cant snap his neck, I still can't understand how the bullet didn't rickashe off his adamantium skull in X2 it just went in, and its a bullet it should have just pinged off
well the bullet did not bounce off his skull because it was shot a very close range and it squeezed inside his skull, like when you shot a sticky gum on a wall at close range, this shows that the adamantium is so hard that the bullet compressed to the point that it had to stick in his skull, if it was faraway, i am sure the bullet would have bounced off.
yes they are not the same but they are related, one is from the other, healing factor is from regeneration. if your body can't regenerate or replace lost or damged tisssues then there can be no healing factor. healing is part of regeneration.