If anything, the second amendment is broader than the first. The first starts out "Congress shall make no law...". The second has no such limitation on who is prohibited from restricting the right of the people to keep and bear arms. Thus while you could argue that the first had to be expanded by the Supreme Court to apply to the other two branches of government or to the states, the second is a blanket prohibition of restriction by all levels and parts of the government from its ratification.
Then why do the gun laws vary from state to state? For example, why is concealed carry allowed in some states but not others if the second amendment applies to every state?
When it comes to the first amendment, the laws in all the states are uniform.