Geometrical tolerances as tricky measurands are indicated. Crucial differences between the ISO and ASME geometrical tolerancing standards are discussed. It is demonstrated that, in many cases, both systems have different default rules. Moreover, for some identical graphical indications, interpretations are different. On the other hand, the standards contain similar arrangements in many cases. It is underlined that nowadays, due to the progressing globalisation, it is necessary to know these standards, bearing in mind that suppliers or customers specify requirements according to provisions from particular standards implemented in their companies. The above justifies the need for research exploring differences and similarities in both systems of standards. It is shown that the ISO GPS system standards, due to default independency principle, prefer to set production as cheaply as possible, while ASME, due to default provisions ( e.g. Rule #1, simultaneous requirement) puts stress on controlling product geometry more strictly, which is sometimes unnecessary.