Here’s a quick summary of New Deal Agencies whose work is related to the Civilian Conservation Corps efforts. More details are on the linked pages. Refer also to the diagram of agency timeframes and relationships. Wikipedia also has pages on these agencies.

1. Emergency Conservation Work (1933) became Civilian Conservation Corps in 1937. It differed from other relief agencies in that it was a residential program (the men living in camps for the duration of their enrollment) and was focused on conservation-related projects.
2. The Civil Works Administration was a short-lived agency that operated simultaneously with FERA, providing relief work for unemployed persons through public work projects. It was liquidated in March 1934, and its functions and records were transferred to the Emergency Relief Program of FERA. [Source: National Archives at 69.2.]
3. The Emergency Relief Administration was formed under President Hoover in 1932, and under Roosevelt was renamed the Federal Emergency Relief Administration. FERA allocated grants to state and local agencies for direct and work relief, set minimum relief standards, and coordinated information on relief problems, policies, and procedures. [Source: National Archives at 69.3.]
4. The Works Progress Administration (formed in May 1935) became the Works Projects Administration (also known as WPA) on July 1, 1939, under the Reorganization Plan. This agency dominated work relief activities and operated through a central administration in Washington, DC, regional offices, state administrations, and district offices. [Source: National Archives at 69.]
5. The Federal Emergency Administration of Public Works (FEAPW) created in 1933 was reorganized into the Public Works Administration (PWA) in July 1939. FEAPW was established by EO 6174, June 16, 1933, pursuant to the National Industrial Recovery Act (48 Stat. 200), same date, to prepare a comprehensive public works program. Renamed PWA and placed under the Federal Works Agency, coordinating agency for federal public works activities, by Reorganization Plan No. I of 1939, effective July 1, 1939. PWA was abolished in 1943. [Source: National Archives at 135.]
6. The WPA and the PWA were both placed under the umbrella of the Federal Works Agency in 1939, along with several other agencies. After 1949, this agency became the Government Services Agency (GSA) and persists today under that name. [Source: National Archives at 162.]