Hi Jaime, "Carry On" can have both positive and negative connotation --> (implication) Example of a Negative implication/connotation: it is not allowed to play loud music after 11 at night. However, my neighbour 'carry on' playing loud music long after 12.00 midnight. Example of Positive implication/connotation: Even though the athlete injured himself, he carried on running to the end of the race. (Carry - >present time and Carried -> past time). "Keep On" generally used in a positive connotations. It does have similar meaning to :carry on" but the positive implication. 'Keep on' will be usually used together with keep on going or keep on doing great job. It is associated with Perseverance and persistence... someone who continue persevere. I hope this was helpful . Ellie :)

carry on = continue (from here) keep on = don't stop (here)

There is no real difference, use them whenever you like.