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one of the countries uses Department and the other uses Ministry, also jurisdictions are different for both of the countries so if I'm writing to (X) Department in one country it would be (Y) Ministry or even (Z) Directorate in another, how to reach a middle point or an equilibrium, noting that my translation will be notarized and certified for both countries?
The best to do is to write to each country in the language you believe applicable to, and between two brackets you add equivalent words in the language of the other country and vise-versa.
my opinion is to write it in english if that is your main language you are experience in it
To avoid any confusion I would suggest you write two different versions , one for each country.
I realise it would appear to double up your workload, but in the long run it will avoid complex,lengthly and expensive legal issues further down the road.
True, many a time such situation persits. But if oneself take proper care and prudent can specify that, the very transalation is for a particular country, than only can resolve problem in future, otherwise, interpretation of law is vary from place to place also.
you can add a numbered reference to the page footer that corrects/change the term used according to the variety you have for that specific term. you don't have to make as many versions of the document.
Use a general term in the document body such as "responsible authority", and in the footer, you list the actual name per country.
You can check the pamphlets of terms produced by language academies to make sure that the terms which you will use in the target language are the accurate, and unified ones
There should be a clause in the contract about dispute resolution. Qualified lawyers/business persons put a clause in case of a conflict; for example "To the extent of any inconsistency between a translated version of this Agreement (if any) and the English version the English version will take precedence.".
So I would change the term according to the meaning in the English(according to the example above) written contract.