care about something—
1. feel anxiety or concern about smth.:
- I’m not sure that anyone in the audience really cares much about what happens to him.
2. take an interest in smth.:
- Jack didn’t care about anything but horses and dogs, and lived every day of his life.
care for something—
1. wish for smth.:
- “Care for a bit of navy plug?” He never dreamt of boarding a trawler without strong navy plug tobacco in his pocket.
2. = care about something 2:
- Do you care for Venetian glass? Ah, not so very much, I see; but you would be converted, I am sure you would, by my chandelier.
3. look after smth.; preserve smth. with care:
- The skilled staff needed not only to maintain the fabric of the buildings but to care for the precious pictures.
Note: The expression does not fully correlate in meaning with the phrase take care of something—
1. = care for something 3:
- Young ladies are delicate plants. They should take care of their health and their complexion.
2. deal with problems, etc.:
- He found himself besieged with petitions for jobs. It was impossible to take care of all of them.