There is no difference. 'Favor' is the American spelling, 'favour' is the British spelling. It's the same word with the same meaning.
2016年5月21日
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Like Paul said, there are several differences between British and American spelling. This, an example of -our words, is one of the most common (favor/favour, color/colour), along with -ise words (like apologise/apologize). This is a good source: http://www.oxforddictionaries.com/us/words/british-and-american-spelling