"look after (someone/something)" and "take care of (someone/something)" are often interchangeable but sometimes one fits the context better than the other. For instance when saying goodbye, you could say "Take care!", but you wouldn't say "Look after!" as it would seem incomplete. You would have to add "yourself" at the end. A correction: The babysitter looks after my baby when i have to work The babysitter cares "FOR" my baby when i have to work. That phrase is incorrect. Correct: "Takes care of my baby", or "cares for my baby." Both work.