What does this feature really do?
I understand the challenge of participating in something like NetPro when English is not your primary language. I feel that you have expressed clearly your question.
It has been a while since I tested this function and so I may not be entirely authoritative. But I believe that the difference is the reaction to situations where the CDP advertisements just stop and where the interface goes down. In the situation where the CDP packets just stop arriving the router should use the holdtime in CDP to maintain information about the neighbor. But when the interface goes down then the router knows that the neighbor is really gone and does not maintain the information for the holdtimer.
You can test this by bringing the serial interface back up, let CDP get established so that both routers see each other as neighbors, and then on R3 on the serial interface configure no cdp enable. This will stop CDP over the interface but will leave the interface up and active. In this case I believe that you will find that R1 maintains the information about R3 for the holdtimer.