This is the question that decides everything else, and the answer is always the same: look at the seal, not the subject matter.
California Secretary of State — birth, marriage, and death certificates issued in California; California court records; anything notarized by a California notary; California business filings; California DMV records.
U.S. Department of State, Washington — FBI background checks, USCIS naturalization and citizenship certificates, Consular Reports of Birth Abroad, IRS and Social Security letters, DD-214s, USPTO records.
Another state — anything issued outside California, no matter where you live now.
We handle all three. But sending a document down the wrong route gets it returned unprocessed, so we check before anything moves.