In several published literatures, some new measurement concepts have been proposed to reinterpret measurement theory, which leads to a new interpretation method of measurement theory. By directly comparing the measurement concept differences between the new theory and the traditional theory, this paper reveals that the root of these differences is due to the different understanding of the mathematical concept of random variable, and clarifies the evolution process of other conceptual differences. Also, by reviewing the mathematical concept, it points out that the traditional theory has been gone astray, and the concept of error classification is actually the product of going astray, while the new concept theory should get active attention and research.