A descriptive essay provides details about your topic; for example, cake designs. You might talk about tiered cakes, shaped cakes and single-layer cakes, as well as the cake pans, tools and techniques for building each. The goal is to help the reader visualize the topic through use of sensory descriptors, such as smell, sight, taste and sound.
A process essay is instructional. You might, for example, explain how to make a birthday cake that is shaped like a train. Your explanation would cover in chronological steps how to prepare the cake batter, bake the cake in specific-shaped pans, assemble the pieces and decorate the cake. The goal is to tell the reader step-by-step how to complete a task.
A compare and contrast essay talks about similarities and differences. For example, you might discuss how the ingredients and baking times for tiered and single-layer birthday cakes might be similar, but how the assembly and storage will differ. The goal is to provide facts about similarities and differences but not to persuade the reader one way or the other.
An argument essay or position paper is designed to support one position over another. For example, you might argue that a homemade birthday cake is superior to a purchased cake because it has fresher, hand-picked ingredients, is cheaper to prepare and has a more personal touch in its preparation. The goal is to persuade the reader to believe what you, the writer, believe about the topic.
An analytical essay gives an unbiased but in-depth explanation of the topic. For example, your essay might examine the advantages and disadvantages, as well as the strengths and weaknesses, of baking a tiered birthday cake. The goal is to provide a fact-based look at the topic so the reader can decide if this is the best choice for him given, for example, his time, experience and budget.
A narrative essay relates your personal experience with the topic. For example, you might have once baked a birthday cake for your child that made both of you very happy for different reasons. The narrative essay tells a story in the "I" voice and is written in a conversational style. The goal is to help the reader come to a conclusion about life based on others' experiences.