Masters of Science in Engineering or M.S. is a research degree.
Masters of Engineering is a professional degree. For reference, it is similar to M. Tech/M. E. degree in India.
While there is not much difference between the scopes of the degrees (both tend to lead to good employment), it is the method of learning that varies between the two.
Before explaining the variances further, let’s clarify two exceptions. In Australia, M. Eng. is research, not a professional degree. The program lasts for two to three years and requires a thesis submission at the end of it. In the U.K., M.Eng. is a five-year course with the last year spent in the industry. At the end of the degree, students become chartered engineers.
To make the difference between the two Masters courses in Engineering simpler, we pick Cornell as an example in this article. It is one of the top universities in the US that offers both the courses.