K.O. is obvious, the guy gets hit, the guy falls down, the guy wakes up in hospital.
T.K.O. is when the fight is stopped because a fighter was getting clobbered and the ref stops it before he is in risk of getting any serious injury.
On occasion a fighter will still pass out even after the ref calls it. Also, more often than not, a T.K.O. is called when the fighter is already in defense on the ground. Most K.O.s occur when a fighter goes from a standing position to a not standing position.
Good luck with all you do. Keep your hands up.