This is probably more info than you want, but:
At the federal level , the prosecutors are the U.S. Attorneys. There is one in each federal court district (each state has somewhere between one and four, depending on population size). His/her Assistant U.S. Attorneys are known as AUSAs.
At the state level, the prosecutors are either chosen on a county basis or on a district basis. In most states, they are called either District Attorneys or State's Attorneys, although some are called by other titles (see: https://en.wikipedia.org/wiki/District_attorney). In states where they are called DA's, like New York, the assistants are ADA's. If they are State's Attorneys, such as in Illinois, then they are ASA's, etc.