Worrying vs. Caring

So I was at the park with my older boy, and I went to sit on this one bench that was in the shade and wasn't hot from the sun shining on it all day. My wife remarks that I cannot clearly see my kid playing from that spot. I said "so?". She asked if I was worried that he might get hurt and I said "no, why would I worry about that?" Then she asks me why I don't care about my kid. I told her I care about him, but I am not going to worry about something that hasn't happened.

So it spurred a thought in my head. Does worrying=caring? Can you care about something and not worry about it? Do women tend to equate worrying with caring more than men? Do liberals/conservatives equate worrying with caring more/less than the other?

I can't be bothered to worry. Stress kills.

I do not think that worrying=caring.

Worrying is something that is passive. It's a thought and can in many cases be destructive.
Caring is not passive but active. Caring is action while worrying is not.

I think that it's impossible to care for someone without worrying about them under certain circumstances, (such as worrying about them when they are sick or something of that nature), but that doesn't mean you have to worry about them all the time in every single situation.

It doesn't have to be all or none. In fact, I don't think it is ever all or none.

Depending on how they are used they can be Synonymous, or that may not be, it depends.