這兩句句子的意思有分別？

care for = look after 照顧
care about = worry about 擔心, 關心

所以,
I had to care for my elderly parents when they both became ill.
比較合適.

care about = to be concerned about what happens to someone, because you like or love them

care for = to do the necessary things for someone who needs help or protection, especially someone who is young, old or ill