It has something to do with citizens. For example firearm ownership and voting are restricted to citizens, not just people-who-happen-to-be-here.

All the constitution has to say on firearm ownership 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.

No mention of citizens.

The constitution does mention citizens

1) Limiting people from congress/senate/president unless they have been citizens for various lengths of time

2) The supreme court applies

3) States can't discriminate between people from one state or another