In most army lists, the term 'standard bearer' is used throughout, though the model in question might actually carry an icon, pennant or other such totem. Similarly, a 'musician' might bear a drum, flute, horn, zither, hurdy-gurdy or some other weird and wonderful instrument – they will still be described as a musician.
Champions differ somewhat – they will often be given a rank or name specific to their unit or army. Whatever this may be, they follow all the rules for a unit champion given here.