I have just been trying to get thing clear in my head re: Italian Air Forces, so I made this mini-table - I know there is no exact definition of this, but is this roughly correct?
Also:
Regia Aeronautica - The 'Royal Air Force' was formed in 1923 and ceased to exist in 1946.
Aeronautica Nazionale Repubblicana - 'National Republican Air Force' was formed during WW2 as the Air Force of the Italian Social Republic, and was closely linked to the Luftwaffe.
Aviazione Cobelligerante Italiana 'The Italian Co-Belligerent Air Force' was formed in 1943 in the South after the Italian Armistice and fought on the Allied side.
Aeronautica Militare - The current Italian Air Force which was formed in 1946 when Italy became a Republic.