Research Paper vs. Thesis
The difference between a research paper and a thesis is that the latter is copyrighted and published on the Morris Library website. It has nothing to do with how profound the work is. For example, a political science student's paper on editorial cartoons from the last 20 years would have to get permission from the copyright holders of any cartoons used. This could take months and be expensive. So the student might want to make it a research paper. But if they did their paper on editorial cartoons from the 1800's the cartoons would be in the public domain and they could make it a thesis.
The advantage to doing a thesis is you can show it off to prospective employers, grad schools and your parents can show it to all their friends. Also, SIU has a best thesis award each year, but not a best research paper award. The one downside is that if you are going on to get a PhD you cannot re-use material in your thesis because it is copyrighted. You can of course still cite it and build on it. If you do a report no one will know. I encourage students to do a thesis.
For reasons that would only make sense to an administrator, if you want to do a research paper you must take Math 598. If you want to do a thesis you must take Math 599. And you cannot change your mind at the last minute.