TF 38 came into existence in August 1943, built around Saratoga (CV-3), and under the command of Rear Admiral Frederic Sherman.
TF 58 was created under the command of Marc Mitscher, on 6 January 1944. TF 38 continued to exist, with a handful of ships assigned, for two reasons. One was to confuse the enemy, and the other was that it was used for planning purposes when not in operational use. The same became true of Task Force 58. It consisted of six aircraft carriers, six light aircraft carriers, and a host of supporting ships.
The force became TF 38 again on 26 August 1944, and grew to nine CVs and eight CVLs in preparation for the landings on Leyte.
It became TF 58 again on 26 January 1945, then back to TF 38 on 25 May 1945, remaining so until the end of the war.