What is the meaning of the word “Al-Salam” in the phrase “Al-Salam Alaykum wa Rahmatullah”? And is it the same meaning as “Al-Salam Alayka Ayyuha An-Nabiy” as one of Allah’s Beautiful Names, meaning The Preserver and The Guarantor?

"Salam" (Peace) is one of the names of Allah the Almighty. In the Tashahhud, "Salam" to a Muslim means supplicating for their protection and care, and that Allah may safeguard them from all afflictions. So, the meaning of "Al-salamu alayka" (Peace be upon you) is: May Allah be your protector and guarantor, or may safety and salvation be for you. "Salam" also means supplicating for safety from every affliction, such as supplicating for safety from illness, insanity, the evil of people, sins, diseases of the hearts, and Hellfire.