If you care for someone, it's your duty to make sure that person is well, safe and fed. You need to be with that person to care for them (and they can't care for themselves). If you care about someone, you often think about that person and hope that he or she is OK. There are a couple of other meanings, but I think this is the main difference.

To care for someone is to look after someone, also to take care of someone (or something): clean them, feed them, keep them safe and happy. Example: my mother cares for my grandmother. My niece cares for her cat. The doctor cares for my health. Who do you care for? Do you care for someone? To care about someone/something is to have an interest in someone/something, and sometimes you worry too. Example: I don't care about the weather. I care about my family. I care about the environment. What do you care about? Do you care about learning English?

This is where the real confusion lies and where the clear definitions of the Oxford Dictionary are helpful: care about - [OFTEN WITH NEGATIVE] Feel concern or interest; attach importance to something. Example: They don’t care about human life. care for - Feel affection or liking. Example: You care very deeply for him. Concern and interest are quite different from affection or liking. That is the difference.

˝Care about˝ is when we take care about someone or something like in this example: She take care about her dog. which means she feed him, washing him, walking him and do everything that it feels good and grow up nice. ˝Care for˝ is similar like worry or mind. At example: She care for her mark. or She care for him. which means that for her mark is important or in second example that his behavior towards her is important to her because she like him. I am also learning English so might I did not give you the best answer but this is my opinion. :)