Is AFL-CIO a government agency

No, it is a private consortium of Labor Unions. The C.I.O is or was the Congress Of Industrial Organizations. Most CIO unions have the Word (United) in the title such as United Mine Workers, United Auto Workers, United Federation of Teachers. They aim at organizing across industries and not specificallly occupationally-skilled crafts such as, say Millwrights or Mechanics. That is the main difference.