You are correct.
But the courts have ruled that the second amendment only applies to federal laws, not state laws. If Mr. Heller resided in Chicago and claimed second amendment protection, the courts would have thrown it out.
Since he is a Washington, DC resident, however, we are talking about federal law and the second amendment.
"The chief difference is that "the right to bear arms" is specifically in the Constitution."
Yes, and so is the right to free speech. Yet some speech is federally regulated even though the first amendment reads, "Congress shall make no law ...". The question to the court is if some weapons can be regulated.
How's it going Robert? Changing your screen name doesn't hide your stripes.