What is the explanation of the hadith: "The one most worthy of Allah's favor is he who initiates the greeting of peace (salam)," and does it mean that the one who initiates the greeting of peace is closer to Allah than the one to whom the greeting of peace is returned?

The first Hadith, "Indeed, the person closest to Allah is the one who initiates the greeting of peace," is a حسن (hasan/good) Hadith. Its meaning is that the one who initiates the greeting of peace is closer to Allah's mercy and greater in reward because he is the first to remember Allah. As for the second Hadith, which specifies the number of mercies, it is very weak. The merit of initiating the greeting of peace does not negate the other party's closeness to Allah or their reward; rather, it is a preference for the initiator because he is the first in obedience, humility, and good character. If a Muslim misses the opportunity to be first this time, he should strive to compensate for that with other good qualities, as was the case with the Companions, may Allah be pleased with them.