Sorry, but i still find it confusing . Giving examples would be better.. Thank you

The two phrasal verbs have more or less the same meaning. When something `cools down' or `cools off', it becomes cooler than what it was earlier. In other words, the temperature drops a little bit. During summer, when it cools down, things seem a little more pleasant. Ex- It was well past midnight before it started to cool off/cool down. The two expressions can be used with people as well. When you say that someone has cooled down/cooled off, what you mean is that he has become less angry. Ex-There's no point talking to you now. Go to your room and cool off.

Cool down can also be something you do after exercising. as in " I usually walk for my cool down. "

it depends on the sentence its used in , cool down usually is associated with saying "when someone is angry they need to "clam down". and cool off is used when its hot outside and you go swimming to "refresh your self". So cool down =calm down, cool off= refresh