both parents work and take care of their family and children

一、care for 中的 care 是动词,表示“把...放在心上”,以下是它的引申意思：
1. 把某个东西放在心上,引申为“喜欢”,如：
I didn't care for the movie I saw yesterday. 我不喜欢昨天看的那个电影.
I don't care for music. 我不爱好音乐.
2. 把某个人放在心上引申为“关心、关怀、照顾”,如：
He cares for no one. 他不关心别人.
3. 把某件事情放在心上引申为“介意、在乎”
Would you care for another helping? 你还介意得到帮助吗?
二、take care of 中的 care 是名词,表示“承担对...的责任”,其引申义如下：
1. 承担对人的责任引申为“照料,赡养,关怀”,如：
My mother is ill. I must ask for a leave to take care of her. 我母亲病了,我必须请假照顾她.
It is your duty to take care of your aged parents. 赡养年迈的双亲是你的义务.
2. 承担对物的责任引申为“看管,维护,保养”,如：
There was something wrong with the machine and the manager asked him to take care of it. 那台机器有点毛病,经理让他维护.
Take care of the pence and the pounds will take care of themselves. [谚]节约每一个铜板, 财富自然会积累起来.
三、care for my son 和 take care of my son 的区别：
1. care for my son 着重于把儿子放在心上,从问寒问暖、关注成长的角度对儿子给予照顾、呵护；
2. take care of my son 着重于承担的义务和责任,从物质供给到精神安慰对儿子进行抚养.