The 2nd. amendment gives all americans the right to keep and bear arms...
The major difference is defined in your own words.
You believe that the government (in this case through the 2nd Amendment) is the defining grantor of your rights.
You simply don't have a clear understanding of the "nature" of rights.
Our rights are ours by birth, by the grace of Providence and the Almighty, and the 2nd Amendment simply acknowledges that The Founders understood the issue well enough to place into the very foundation of our law an article forbidding government at any level to infringe on that right.
No government at any level may assume authority to dictate what a free man may, or may not, do with regard to arms.
While most government chooses to ignore the fact,
it's the law. Any law published afterward that is contrary to that law is voided at it's inception. That's the law too.