I think that’s the distinction I basically make. Buttercream? Frosting. Does it involve cream cheese? Frosting. Is it just basically powdered sugar and milk or cream? Icing. Can you pour it? Icing. Only spread it? Frosting.
I think you’re referring to “rolled fondant”, which has a lot of other stuff in it making it kind of like clay and not pleasant to eat. Most people eat around it. It’s rolled out into a flat layer and draped over a cake with the sides pressed flat. Then it gets decorated.
Royal icing is what you see on decorated cookies and lace work on wedding cakes.
Don’t make that “marshmallow” frosting then. It’s basically pure SWEET (though it can be jazzed up a bit with different extracts, and the time I served it with peppermint sprinkles it was a real hit).
It definitely doesn’t have the same satisfaction or mouthfeel as a halfway decent buttercream.
Example of what fondant looks like: Satin Ice 5 lb. Red Vanilla Rolled Fondant Icing (webstaurantstore.com)
It’s what you’ll see on bakery sites for really fancy decorated cakes. It’s perfectly edible, but not tasty. You can also make a sort of fondant from scratch using melted marshmallows and additional sugar, I think.
Royal icing is quite different.
You can make it with meringue powder (which is basically powdered egg whites); I think you can also make it from scratch starting with egg whites, but the one time I ever made royal icing, I used the meringue powder.
Specifically, fondant contains the basic buttercream ingredients (confectioners’ sugar, some form of shortening, vanilla) along with small amounts of gelatin, glycerin, and glucose syrup to provide the pliable texture.
It can be flavored, like any other frosting/icing. Personally, I find (good-quality) fondant just as edible as any other (very sweet) frosting/icing, though I get it if the more marzipan-like texture is off-putting to people who were expecting a more “frosting-y” fluffier buttercreamish mouthfeel.