"Undergraduate thesis" and "Final Paper" Final Paper is a general decription. It can be the last paper you write for a class or a last paper you write at the end of a school year. An Undergraduate thesis is specific. It is the paper you write, in whatever your major is, so that you can graduate. You are then awarded a Bachelor's degree. And a graduate thesis is what you write to earn your Master's degree. Hope that helps. :-)

Final paper could be just the final exam for a single class. It could also mean the final paper for your whole schooling carrier. It depends on the context of the conversation. An undergraduate thesis is the culmination of a college experience. It is not always required depending on the school and or field of study.