Another example to help differentiate between the two is an explosive decompression. The crew would initiate an "emergency descent" but if they suspect airframe damage they may consider maintaining the current speed and aircraft config (i.e: no speed brake or gear) to avoid further damage. On the A320 this would give a rate of descent of around 1500-1800fpm - an emergency descent but not a rapid descent.
Hope that helps.
Cheers
Pro Spin