CJS is 100% correct for RI.
In that 7 day wait if you do not have a CCW, the selling FFL dealer sends a copy of your purchase to his/her towns Police Chief. The thought is that the there might be pending restriction that the NICS may not have been updated on, e.g. domestic abuse, restraining order, etc.
In PA. it is immediate post the NICS check when purchased through a FFL dealer for long and/or short guns.
Each state is different.