The MAIN difference here is that GUN RIGHTS are specifically spelled out under the Constitution. If you bother to look even further, and read the Federalist Papers (documents and thought by the founding fathers), you will clearly read that The Founding Fathers of the United States firmly believed it was the right and responsibility of every Citizen to stand against tyranny, and gun ownership was a necessary balance as the last step against a corrupt Government.
The vast majority of Americans who cite the second amendment to me can't even tell me what it says word for word , they can't even convey the general gist of it which is douby funny, firstly, because the 2nd amendment is only one sentence, and secondly because I can recite it word for word and I'm not even an American citizen. What they usually regurgitate is something that boils down to this:
"It being of paramount importance that all citizens of the United States including robbers, pirates, dealers of addictive narcotics, other members of the criminal class and the nations various types of bat shit crazy lunatic have full and unrestricted access to guns there shall be no attempt by the government to control gun ownership or to monitor it in any way. Furthermore the government shall also be forbidden to mandate that gun owners show that they are well trained and disciplined users of firearms as a precondition for owning a firearm."
What the second amendment actually says is:
"A well regulated militia being necessary to the security of a free state, the right of the people to keep and bear arms shall not be infringed."
What that means is that the constitution guarantees the right of US citizens to own a gun for the purpose of forming a 'well regulated', meaning well disciplined and trained, militia. That's all the 2nd amendment says. Today the largest examples of the kind of militias that the writers of the second amendment had in mind is commonly known as the 'United States National Guard' although the second amendment does arguably also allow states to operate their own militias as long as they are 'well regulated'. The most interesting aspect of this is that the US government could under the second amendment mandate that all aspiring gun owners undergo a training course in fire arms operation prior to acquiring their first gun since the second amendment does say 'well regulated' which effectively means as I pointed out before 'well trained and disciplined'. Furthermore the 2nd amendment might also allow the government to reject people who it deems to be insufficiently disciplined to be part of any 'well regulated' militia.