The Army Air Force was so called until 1947, when the U.S. Air Force as a separate service was established.

The song beginning "Off we go" is distinct from the one beginning "Into the air", both in words and in music.

Incidentally, from my childhood during W.W. II, I remembered the third line of the former as "Up we go, ready to mete out thunder". Later in life, I was amused by the sudden change in register between "mete out" & "attaboy". But recently I looked up the matter on Google & concluded that "mete out" must have been my imagination.