Ok. I don't know if there may be a bug involved or not. Here's my testing with the current stable version:
With "Prevent sharing...." unchecked, allowing sharing of gradient defs, when you duplicate an object, it gets the exact same gradient. If you edit the gradient in the original object, it gets edited in the duplicated object.
When the original object with gradient is copied and pasted, the copy/pasted object gets a new gradient number. Well it's the same number with a dash and another number, such as 1234-4. But when the gradient in the original object is edited, it's not changed in the copy/pasted object.
With "Prevent sharing...." checked, and you duplicate an object, it does get a gradient with the same number ID as the original object. But when you edit the gradient in the original object, the gradient in the duplicated object does not change. And at the moment you edit the original gradient, it gets a new ID number. The duplicated object's gradient does not change, and retains the original ID number.
When the original object is copy/pasted, it's the same, whether gradients are set to be shared or not.
It does seem odd to me, that when "Prevent gradient def sharing" is checked, when you duplicate an object, its gradient has the same ID number as the original. It would seem to me more logical if the duplicate got a new ID number, at the moment of duplication. Perhaps that part is a bug, I don't know. But the way it is, whichever gradient is edited gets the new ID number. That does make sense. I agree that the duplicate initially getting the same ID number seems confusing. But I guess it's because, until one of the 2 objects' gradients is edited, the ARE the same gradient.
Duplicate and Copy are NOT the same thing. If they were the same thing, there wouldn't be any use for one or the other. But since they both exist in Inkscape, it makes sense that they are different, in some way. I can't explain, technically.....or even simply (lol)) what is the difference. But I would not expect them to necessarily act the same way, even though they seem to do very similar things.
Opps, 2 more messages while I'm typing.
Moving the end stops of a gradient does not make it a new gradient (when Prevent Sharing is enabled). I can't explain why. Maybe bug, I don't know.
(You can search the bug tracker, if you're interested.
https://launchpad.net/inkscape)
Yes, if you want global editing, you'll need to use clones.