Yes, there is. It depends on the context or what the person really wants to say. Sometimes it also applies as a synonym but sometime it doesn't. There is no perfect way to explain it without examples so I'll try my best:
1: Kind of different meanings
- I care for that project (it's really important for you)
- I take care of that project (you take it over)
- I care about that project (you worry about it)
2: Similar meanings
- I will care for my brother during the day (same as take care of)
- I take care of my brother during the day (same as care for)
- I will care about my brother today (similar but like you will pay attention to him)
There will probably be more better examples. I hope this helped you a little