Cakelike brownies are really… well, little cakes! They contain less butter and more flour than fudgy brownies, as well as a bit of baking powder to make them softer and lighter. Often the softened butter is creamed with the sugar rather than melted with the chocolate. (Creaming incorporates air into the mixture, which causes the brownies to rise higher.) Many cakelike recipes also call for a bit of milk to add tenderness.
Chewy brownies usually get their texture from two factors: an extra egg (or even two) and a combination of different types of chocolate. Of all the chocolate types, unsweetened chocolate has the highest proportion of starches, which create a stiffer-textured brownie. Semisweet chocolate produces a creamier texture. Put the two together, often with a few tablespoons of cocoa powder to round out the flavor and thicken the texture, and you get a rich, satisfyingly chewy result.
Blondies are really butterscotch bars, made with brown sugar, butter, and eggs (and usually nuts as well), but no chocolate. Typically, blondies have a cakelike texture.