وَعَلَى آلِهِ
And upon his family.
Depending on context, āl may refer to a family line, the Prophet's household, or in broader usage those associated with or following him. Scholars discuss its precise scope in different contexts; it is therefore unwise to impose one restricted definition on every occurrence.
In the formula of blessings, invoking goodness upon the āl of Muhammad ﷺ expresses reverence and prayer for those specially related to him. It is part of the etiquette of honoring the Messenger.
Principle: Genealogical relationship, religious following, and technical usage are distinct considerations. One lexical meaning alone does not settle every theological or legal application of the term.