Purpose and theme are related. Our theme is the main point that we want to communicate. Our purpose is the reason we want to communicate that point. Stated another way, theme is what we want to communicate and purpose is why we want to communicate it.
There are many possible purposes. We may want to convince the reader of our viewpoint on an issue. We may want to provide the reader with information. We may simply want to express our opinion on something, such as a book or movie review. We may want to entertain. Our purpose may include several of these. Each of these purposes are valid, and the purpose that we select will influence what and how we write.
For example, if we are trying to convince the reader of our viewpoint, we will present facts that support our position. However, if we are trying to entertain, we might use the same facts but exaggerate them or use humor to illustrate an absurdity.