In many states, there is no difference - they are one and the same. In Connecticut, however, the Attorney General exercises only civil jurisdiction. That means his office is basically in the business of bringing lawsuits in the civil courts, or to defend the State when it is sued. With very few limited exceptions the Attorney General has no jurisdiction whatsoever over criminal matters and no authority to prosecute criminal violations of the law.
The state Constitution places the sole responsibility for the prosecution of all criminal matters with the Division of Criminal Justice, i.e., the Chief State's Attorney and the thirteen State's Attorneys. The Chief State's Attorney, may, however, as he deems appropriate, designate the Attorney General to handle specific criminal cases on a case-by-case basis. Again, this occurs only under very limited circumstances.