the "same service programs" refers to the ISR(Interrupt service routine) which is executed when interrupt is raised.
since interrupt is raised from single interrupt request line to which many devices are connected. If more than one device raises an interrupt , a priority or first come first serve basis may be decided for servicing the devices. So polling is a method in which the servicing is done by checking each device for possible interrupt request. Any device which is found requesting service , it's subroutine is executed by branching from the original ISR , in which conditional branching code for the devices will be contained.