In most army books, the term standard bearer is used throughout, though the model in question might actually be carrying an icon, pennant or other such token. Similarly, a musician might be carrying a drum, horn, zither, hurdy-gurdy or some other weird and wonderful instrument – they will still be described as a musician.
Champions, however, are different. You'll rarely find a champion option referred to as simply a champion – he'll be listed under the rank or name given to the champion of that particular unit. There is a little potential for confusion here, as a champion is not so clearly identified as a standard bearer or a musician. Fortunately, this distinction makes the champion easy to identify – if a unit has a champion option, it'll be the one that isn't clearly labelled musician or standard bearer. Furthermore, a champion always has a slightly different characteristic profile to the other troops in a unit, so if in doubt you can always identify them that way!