A thesis statement is a succinct statement of the arguments you'll be making in a paper and is a critical component of any well-written work. A general statement, by contrast, is any declarative sentence providing supporting information or transitioning to a new topic. While both sentence structures play an important role in writing, a paper without a thesis statement can end up poorly organized with no central argument.
Role in Paper
Your thesis defines the topic and focus of your paper. Even if your paper is not an argumentative paper, you'll still need a thesis that defines your scope. For example, in a paper summarizing "Romeo and Juliet," your thesis might briefly outline three general plot themes. Your general statements should then expand upon your thesis by giving supplemental information and commentary. In some papers, the primary thesis is in the first paragraph, and then each subsequent paragraph contains a mini-thesis. For example, the "Romeo and Juliet" paper might use one paragraph to outline each plot theme, with a mini-thesis at the beginning of the paragraph providing more information about the plot theme.
Your thesis makes a central argument upon which your paper will focus. General statements either lead up to this argument by providing background information or support the argument by presenting and analyzing data. General statements are also an important part of a conclusion. You can use them to outline directions for future research or to address unsettled research debates, for example. Some students mistakenly make a general statement when they need to make a thesis statement. For example, "Poverty is a social problem" is a general statement that does not outline an argument. On the other hand, "School programs designed to counteract the effect of poverty can help undermine the long-lasting effects of low family income" is a compelling thesis statement.
Both your thesis statement and general statements play roles in structuring your paper. Your thesis limits your focus to a single argument or two, and general statements support this argument. In a sociology paper, your thesis might argue that childhood poverty is the best predictor of adult poverty. General statements might then give facts about childhood poverty, statements about how to end poverty or information on the psychological ramifications of poverty. However, your general statements should not veer outside of the limited focus of your thesis. A paragraph full of general statements about how teen pregnancy contributes to poverty would likely confuse the focus of your paper.
Supporting the Thesis
The primary role of a general statement is to support your thesis. In the introductory paragraph, general statements can also build up to your thesis by providing relevant background. You might, for example, make the general statement that "Philosophers have long debated when it is ethical to kill someone," then follow up with a thesis explaining when killing is ethical or how a particular philosopher attacks this ethical dilemma.