air force vs armed forces

air force

noun
  • A branch of the military mainly devoted to air warfare, as opposed to (land) army and navy. 

  • A unit in the U.S. Air Force larger than a division but smaller than a command. 

armed forces

noun
  • The military forces of a nation, such as the army, navy, air force, marines, and sometimes, coastguard or border guard, which are tasked with the defence of the nation and its citizens, if necessary through use of deadly force. 

How often have the words air force and armed forces occurred in a corpus of books? (source: Google Ngram Viewer )