Okay, after a bit of research I found that Constitutionally speaking there is zero difference between a State and a Commonwealth.
Originally the four Commonwealth States (MA, PA, VA, KY) were called "Commonwealth" to denote that they are democratically elected leaders and ruled by "the people" rather than a King or Tyrant.
So, when the US finally realized the insufferable tyranny of extra "u"s in all the words like "colour", they called themselves commonwealths in the hotbeds of revolution, PA, VA, and MA. As for KY, since they were originally just a huge District in Virginia (Ever wonder where District of Columbia came from and why it was a "district"?), when they decided they wanted to keep their whiskey to themselves they held on to the "Commonwealth" name.
Now, there are two other commonwealths under US jurisdiction, but in the case of Puerto Rico and the North Mariana Islands they are called commonwealths because they do have some standing and protections granted them, but do not have the full benefits of Statehood in the Union.
(When West "by Gawd" Virginia seceded from Virginia, they decided to take on Statehood rather than maintain commonwealth...)