In the Czech Republic – as a EU Member State – the MDR standard was implemented under the EU’s binding DAC6 (Directive 2018/822/EU). In case the reference to DAC6 directive is made in the following answers such reference relates also to the Czech Republic MDR implementation without any distinction. 
The main difference between the OECD MDR standard and its EU DAC6 counterpart is that DAC6 regulation focuses specifically on cross-border arrangements that involve at least one EU Member State. Therefore, the applicability of MDR is limited only to arrangements which are related only to the EU internal market. Furthermore, DAC6 mandates automatic exchange of all reported arrangements between EU Member States, ensuring that information circulates across the Union.
The other differences are mentioned in the following answers.