Very little difference, and they can be used interchangeably in many situations. "Favor" usually refers to a specific task or action. "Please do me a favor and drive me to the train station today." This is a specific action and would involve a specific time frame. "Help" can be a broader range of options and stretch over a longer period of time. "Can you please help me to learn Japanese?" This is a larger request, requires more effort on the part of the helper, and can stretch over a broader period of time. These are, of course, only general guidelines and many exceptions exist.

favor- a kind or helpful act that you can do for someone help- assistance, usually in a task