difference between keep and keep on

• you were right. Both "keep talking" and "keep on talking" are correct.

• 'Keep talking' means the same as 'keep on talking'. 'Keep fighting for your cause.' means the same as 'Keep on fighting for your cause.' 'Keep' and 'keep on in these cases are interchangeable and suggest that one must persevere in an action. If you tell someone, "Keep working hard!' or "Keep on working hard." you are encouraging them in something that requires perseverance. 
  
  Whereas the other way of using 'keep' is to guard 'something' such as an object or a secret or thought. "Keep your porch light on at night." "Keep the money in your wallet." "Keep your thoughts to yourself."
  "Can you keep a secret?" You can never use 'keep on' in these circumstances.