Salam alaykum Sheikh.
I would like to ask that what is the correct meaning of Aale Muhammad in Salawat. Does it mean family of Muhammad(peace be upon him) or does it mean righteous followers of Muhammad (peace be upon him) ?
wa `alaykum salam,
Aali Muhammad in salawat means the Holy Prophet Muhammad’s (s):
1) children and descendants;
3) The Banu Hashim and the Banu al-Muttalib.
We are ordered to invoke blessings on the Family of the Prophet including his wives. When the Companions asked the Prophet how they should invoke blessings on him, he said:
Say: “O Allah, bless Muhammad, his wives, and his offspring as you blessed Ibrahim; and further grant blessing on Muhammad, his wives, and his offspring, as you granted blessing on Ibrahim. Verily, Yours is all the Majesty and Glory.”
It is narrated by Bukhari with two chains, Nasa’i, Abu Dawud, Ahmad, Ibn Majah, and Malik.
However, as you mentioned, all of the Ummah maybe considered Aali Muhammad, but not in the technical sense (cannot receive zakat, etc.).
See “Who are Ahl al-Bayt” at the ASFA website for more details in answering this question.