Technically, an amuse-bouche should be a single bite, and you serve just one to a person. The french translates to "mouth tease".
An hors d'eouvre can be a little bigger (2-3 bites max), but people get to help themselves to as many as they wish. They are finger (or toothpick) foods.
An appetizer can be a little larger, and people receive a larger portion at the table. They usually require silverware of some sort.
In real life, the latter two terms tend to be used interchangeably. But amuse-bouche is still only used for that single bite.