Are the effective communication requirements different for a state or local government than for a private business? 

State and local governments must give primary consideration to what the person with a disability requests.  So if this same person who is Deaf plans to attend a City Council meeting and requests an interpreter, the city must provide it unless doing that would somehow be impossible - maybe because the request was just made the morning of the meeting and no interpreter could be found on such short notice.  However, the city must make a good faith effort to secure the services of an interpreter.

Also, although the person who is Deaf does have the right to a qualified interpreter, they do not have the right to insist on a specific interpreter. A qualified interpreter is: a) someone who understands the signs used by the individual who is Deaf and can tell the hearing people what the person is communicating; and b) understands the words being spoken by the hearing people and can convey those words and concepts into signs understood by the people who are Deaf; and c) is objective in the situation.