The purpose of a paper reveals the writer's intention, whether this is to express his feelings, inform readers about a specific topic or argue on an issue and persuade the audience. In an essay, a goal-oriented purpose statement narrows the focus of the subject -- the most general statement of the topic -- and appears in the introductory paragraph, before the thesis. It will often begin with something like "The aim of this paper is to...."
The thesis is a sentence making an assertion on a specific issue and presenting how the contents of the main part are going to unfold. An example of a thesis can be "The United States offers more opportunities to open a small business than Canada." A thesis statement is focused and specific and sets the boundaries for the paper. Theses usually appear at the end of a paper's first paragraph.
The thesis explains what the paper is about, the specific issues it touches and the scope. On the other hand, a purpose statement explains the reason the writer focuses on these specific issues. In simpler words, the thesis statement answers to the question "what?" and the purpose statement answer "why?" However, both statements revolve around the paper's topic and their job is to inform readers about a paper's scope. In the previous example, the "why" before the thesis could be "The goal of this paper is to show how lack of excessive regulations on incorporation and taxation can help an entrepreneur make his first steps."
A purpose statement on a research paper of historical events can be "The aim of the paper is to show how political decisions can have a direct impact on the economic life of the country." Further down the introduction you can add the thesis "President Jackson's tenure had a significant effect on the central banking system of the United States." This way, you show both what the focus of the paper is and why you chose that focus.