what's the difference between vengeance and revenge?

LONGMAN DICTIONARY OF CONTEMPORARY ENGLISH says;

revenge:punishment given to someone in return for harm done to oneself

vengeance:punishment given to someone in return for harm done to oneself,one's family,etc.

we took revenge on them by bombimg their cities.

he swore to take vengeance on the people who had killed her sister.

...I'm really sorry.