Error vs Uncertainty: mathematical, terminological and conceptual aspects of evaluating the characteristics of measurement accuracy

A comparison of two approaches to measurements accuracy evaluation is carried out: the theory of errors and the uncertainty concept. It is shown that, conceptually, the difference between these approaches is reduced to the difference in coordinate systems relative to which the true and measured values of the measurand are considered. The classification of errors and uncertainties is given and the difference between them is shown. The characteristics of the error and uncertainty, and the methods of their evaluation are compared. The comparison of mathematical expressions for confidence limits of error and expanded uncertainty is made. The limitations of both approaches are given. The drawbacks of the concept accuracy evaluation and the ways of their improvement are considered.