wish and wish for

Hello guys,
I need some help for I’ve been trying to find the difference (if there is) between wish and wish for. Check out the examples below:

“Be careful what you wish.” ( is this ex. correct?)
“Be careful what you wish for.”
“I wish a new car.”
“I wish for a new car.”

I know it’s kind a boring and probably retarted question, so I do apologize in advance because of that.

Kind regards,

PredatorTheSkullCollector

‘Wish’ + ‘that’ clause
‘Wish for’ + noun

I wish that I were king.
I wish for a new bike.
I wish for everyone to have a good day.
I wish that everyone have/has a good day.

Thanks for your answer. Now it makes sense to me.
Kind regards,
PredatorTheSkullCollector