It rains cats and dogs.

It rains very hard.
It rains very heavily.

(Are they all the same? Why do we use 'cats and dogs'? Would you let me know the origin of the expression?)

All are about the same, yes. The term "raining cats and dogs" is an idiom. Be sure to read about it in the first couple of links here:

http://www.google.com/search?hl=en&q=raining+cats+and+dogs+metaphor&aq=1&aqi=g10&aql=&oq=raining+cats+and&gs_rfai=