Let me set this clear, because I did this same talk yesterday. Monsters are considered the ones who don't have any power (refering to money) or a title.
Most of the creatures of the show could be considered as monsters, but they're princesses or they're part of an association (Hekapoo, Lekmet, Rhombulus, Omnitrixis) if we consider them as magical creatures they have a task to make what makes them NOT monsters.
But also at River's party in "Royal Pain" we can tell some of the kings could be considered as "monsters" but still, they have a title and they're part of the royal family of some kingdom.
It doesn't exactly refer to the appearance they refer to power and also maybe to a job, we can see those considered monsters are only thiefs, and henchmen, which can cause damage. Not as the alternate monster who seem that don't want to have violence.
If anyone agrees or desagrees, let's have arguments. I want to talk seriously.