I am not absolutely sure. But I think it depends on the sentence. For example: You would use "care about" when you say: "I care about you." Or "I don't care about that!" You would use "care of" when you say: "Please take care of my cat." The "about" in "care about" is representing a subject, such as a type of situation. In this case, the sentence "I don't care about that!" Would mean that you don't care about that situation. The "of" in "care of" is representing some sort of object/thing. so in this case, the word "of" in the sentence: "please take care of my cat" is representing the "cat".

The expressions "care about someone" and "care for someone" are roughly equivalent, but "care of" by itself is non-sensical.

Could you write a couple of examples?

the same meaning *

I want to know too. i remember that article on google said that the two of them have the same meanings but the difference is between "care about " and "care for" .