What's the difference between No Bonus, Fresh Bonus, and Bonus?

No Bonus means you are not allowed to have any items from the bonus shop when you do your run. Fresh bonus means you start off with no bonus points, nor anything bought from the bonus shop and perform the run. The easiest way to do this is to reset all of your progress in options, unlike other runs where it starts when you click "story mode" or "classic mode", fresh bonus starts on the selection between starting muted or unmuted because you can get bonus points in the menu. Bonus means that you can have whatever you want from the bonus shop.

Ah, ok! Thanks for the explanation.