Extra course of fun food, usually involving unusual flavor combinations or textures, formally presented and served, outside of the hors d'oeuvre, served at restaurants that want to provide traditionally served haute cuisine, but with a little jolt of el Bulli-like improvisation. Home cooks, who having been served such at a restaurant they consider a little above their station, may decide that one (or several!) of these items might convey a sense of gravitas to the occasion when they cook themselves, are sorely misled, especially when American restaurants offer an "amuse-bouche" menu with platefuls of food that would otherwise be considered hors d'oeuvres or even main courses in themselves.
Here are the salient differences: an hors d'oeuvre is a separate course, either a soup, a salad, or finger food. You order it, you pay for it. An amuse gueule (no matter which kind of mouth you put it in), is just that: a mouthful, off the menu. The idea is, the cook just happened to have a few dozen pigeon's hearts, be experimenting with the Methocel, or thought it was a keen idea to put caviar and white chocolate together, and let you have it, hope you like it, no extra charge. (In plainer English, it's a great way to float trial balloons over the patronage without having to blatantly waste food.) To plan to do this in a home environment, as part of "formal dinner", just doesn't work...it's like when you were in college, and on graduation, you wanted to 'spontaneously' jump into the fountain, but only right when a)you had your best clothes on b)everyone could see you and c) someone had a camera.
Trying to impress your guests with the fiction that, in between plating the soup, serving cocktails and replying to so-and-so's witty barbs that you just happened to have accidentally made miniature cream puffs with parmesan crisps and white asparagus jelly strains even the politest standards of credulity.