Yes, there are significant differences between testing and quality assurance. Software testing finds faults in the software product by inspecting and testing it. Software quality assurance prevents faults in the software product by inspecting and testing the software development process.
Quality assurance (QA) assists with software development throughout the entire process, from the requirements phase to post-release. This ensures potential problems are identified early in the process, which improves the quality of the final product and allows developers to focus more on improving the functionality and polish of the software, and less on fixing faults in the software. The software is then tested as part of the QA process near the end of the development process, to find any faults in the software which will then be prioritized and eventually fixed (and re-tested to verify the fixes).
Software testing, on the other hand, only assists software development near the end of the development process. Testing by itself is not as efficient as QA in ensuring a quality final product. Without QA, more preventable issues will make it to the software testing stage, which means developers will have to focus more on fixing software faults than on improving functionality and polish. This also results in more time required to be spent testing than anticipated, which pushes out the anticipated release date and/or ensures the software will be released with known or, worse, unknown faults. The software will also be tested to ensure it conforms to the requirements, but if any requirements are faulty, then the software could pass the relevant tests; resulting in undesired software behavior, and it is often too late to modify the requirements at this stage if it becomes obvious that the requirements are faulty.