What is meant by "the Household of Muhammad" in the supplication upon the Prophet: Does it include all Muslims or only the descendants of the Messenger?

Scholars have differed regarding the exact definition of "Ahl al-Bayt" (people of the house) of Prophet Muhammad, peace and blessings be upon him. The most preponderant opinion is that they are Banu Hashim, Banu al-Muttalib, and his wives, peace and blessings be upon him. Banu Hashim and Banu al-Muttalib are considered one and the same, based on the Prophet's saying, "Indeed, Banu al-Muttalib and Banu Hashim are one and the same." As for his wives, it is due to the Almighty's saying, "Indeed, Allah intends only to remove from you the impurity [of sin], O people of the [Prophet's] household, and to purify you with [complete] purification" (Quran 33:33). And they were the cause of the revelation of this verse.