Cake has basically 2 classes, and then of course variations of those classes :
Sponge Cake –
Also known as foaming method cakes, which rely primarily on trapped air in the foamed eggs. Typically Sponge cakes are accompanied by a Simple Syrup which is brushed on the layers to add moisture and flavor to the cake.
Butter Cake –
Also known as Pound Cake and some variations of the Devils Food Cake are mainly creamed butter cakes. Where the butter and sugar is creamed to create a fluffy matrix of air pockets trapping the sugars within the fat pockets. Creamed cake batters have a closer, denser crumb than those recipes which require foaming.
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Then there is a separate class of cakes that fall in a category with
Muffins and Quickbreads
This method typically will ask for the oil and sugar and eggs to be combined together, and then the dry ingredients are added to this.
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You can get a dynamic list of Cakes from this link.