A simple bow is a bowing of the head, whereas a solemn bow is bowing at the waist. Both are a universal signs of honor and respect.
It is an old custom to make a simple bow at the Name of Jesus when you are standing. This pays homage to the Verse in Philippians that tells us that at the Name of Jesus every knee shall bow and every tongue confess. If you are already kneeling it is not necessary to make a simple bow because in kneeling you are already showing Him respect. “Let all that is within me bless His holy Name” Ps 103