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.
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.
You can get a dynamic list of Cakes from this link.