Thank you for your inquery. 

Here is our official answer: 

"States" in "the United States of America", as you mention, mean 
states as administrative and geographical regions of the United 
States, not meaning or implying people or groups of people living 
in the United States in this case. 

Therefore, "the United States" is a union of 50 administrative 
states in the United States. 

Also therefore, if the Japanese character you said does not carry 
the meaning of "a (administrative) state(s)", that is a possible 
translation error. Translates of both "the United States" and 
"the State of New York" should have an identical character(s) in 
them. 

We hope this helps. 

Thank you.