A rental assigns the number to you for the chosen period — from a day to six months. Throughout that time the number receives SMS with no limit on count, and nobody else gets it.
An activation is a one-time service for a single code in the chosen service and country. The wait for the code is capped at 20 minutes, after which the number is no longer yours. An activation is cheaper, but it only suits a registration after which you will not need the number again.