If you choose to follow a list, it will be added to your Saved Locations, under Shared with me, where you will be able to view it and see the updates the list creator makes to it. You won’t be able to edit it.

If you choose to save a copy of a list, it will be added to your Saved Locations, under My lists. You will be able to edit it but you won’t see any of the changes the original list creator makes in the future.