American Buttercream-
When you think of cake icing, this is probably the one you think of. This simple mixture of softened whipped butter, powdered sugar, and flavoring makes a simple and foolproof icing. The key here is making sure your butter is incredibly soft, but not melted.
Cream cheese frosting is a derivative of american buttercream, simply mix in half butter and half cream cheese, also held at room temperature.
European Buttercream-
The difference between American buttercream and European buttercream icings is the addition of meringue. Meringue, (whipped egg whites and sugar) adds body, stability, and whipped texture to the frosting. The meringue is made first, then softened butter is whipped in slowly (as to not deflate the meringue) and whipped until the desired texture is reached.
Swiss buttercream is made with egg whites and sugar, warmed over a water bath so the sugar dissolves, resulting in a smooth texture. Italian buttercream is made with cooked sugar, and the liquid sugar is folded into the egg whites to create a more satiny texture.
Glaze-
Glaze doesn’t have air added into it the way that these butter based frostings do. Most glazes are powdered sugar based, thinned out with a liquid such as cream, milk, water, or juice. The more liquid you add, the thinner the glaze will be.
Whipped Creams-
Whipped cream frosting is incredibly simple: just whipped cream and sugar and/or flavoring. When the cream is flavored, it is called “chantilly cream,” and the key here is to keep your cream cold so it whips up to maximum volume. However, whip your cream too much and it will turn into butter!
Ganache-
Ganache is a mixture of cream and chocolate. The cream is heated, then the hot cream melts the chocolate to create a thick but fluid mixture. The ratio of cream to chocolate depends on the texture you want, and for frosting, you do less cream to create a more solid and spreadable ganache.