The winged propeller is the branch insignia for the Army Air Corps, not to be confused with the organization under which personnel assigned the branch operated, the Army Air Forces. For all intents and purposes, they were the same, but, really there is a big difference between branch and organization. For example, infantry is a branch, and during the WW2 period was part of the Army Ground Forces. Anyway the winged prop is the branch insignia worn by USAAF enlisted personnel.
The other insignia is the distinctive unit insignia for the Air Transport Command.
Later . . .
See http://blog.medalsofamerica.com/air-transport-command-atc/ to show how insignia are worn. US and winged prop go on collar points of blouse, US right, winged prop left; ATC unit insignia goes on lapels, both sides. Usually not worn overseas and especially in combat areas.