In English you can use the verb “to bake” both for cakes and bread.
In Korean, the verb for baking, 굽다, is used for bread, while cakes are ‘made’.
My language partner said I could think of it this way:
When you bake bread, you mix some things together, but the oven will finish the job.
When you make a cake it can be rather elaborate work. Even if you need to bake some “elements” of the cake, that may just be preparation. Perhaps you still have to put the things together, decorate it and so on. This is something that we do, not the oven so therefore we make cakes, we don’t bake them.