Longman Dictionary of Contemporary English in a THESAURUS section for "hurry" defines/compares "hurry" and "rush" as follows:
hurry: to go somewhere or do something more quickly than usual, for example because you are late or you must finish something soon
If you don’t hurry, you’ll miss the bus.
We have plenty of time. There’s no need to hurry.
rush: to go somewhere very quickly, or to do something too quickly and without thinking carefully enough
Everyone rushed out into the street to see what was happening.
Try to answer the questions calmly, without rushing.
A police car rushed past.
In a THESAURUS section for "rush" it defines/compares "hurry" and "rush" as follows:
rush: to move very quickly, especially because you need to be somewhere soon
He was rushing out of his office in order to go to a meeting.
There’s no need to rush - we have plenty of time.
hurry: to do something or go somewhere more quickly than usual, especially because there is not much time
People hurried into stores to escape the rain.
You ll have to hurry or we 'll be late for breakfast
I hurried through the rest of my workout and showered as quickly as I could.
Actually, I don't get the point! It seems that they can be used interchangeably. If it is not the case, then when should I use hurry and when should I use rush?