At burial the wording is بِسْمِ اللَّهِ وَعَلَى مِلَّةِ رَسُولِ اللَّهِ
Translation: In the name of Allah, and upon the religion of the Messenger of Allah.
Other transmissions have the wording ‘ala sunnat Rasul Allah. Millah refers to the faith and path; sunnah emphasizes the Prophetic way. These are variant transmitted wordings, not competing rituals.