Don't quite get the music

It was great to see barak Obama's inauguration, but I'm bemused about the music used. First Aretha Franklin sings a song that was announced as the national anthem, but it clearly wasn't, instead it was something to the tune of the British national anthem "God Save the Queen"! Then those very talented musicians played a tune said to be a composition by John Williams, but it was clearly a variation on Sydney Carter's "Lord of the Dance"! Wierd!