They later expanded upon it in McDonald v City of Chicago.
L
Yes, you are correct.
In the McDonald (2010) case, the Court ruled that the Second Amendment applies to state and local governments. I would note that he District of Columbia is part of the federal government and thus the Court had no occasion (in the Heller case) to consider that the Second Amendment applies to state and local governments.
That said, what is also important to point out is that in terms of the Heller and McDonald cases, the Court focused only laws associated with the prohibition of virtually all possession of handguns. The Court had no occasion to consider the constitutionality of more limited regulations.
LR