What would be the difference between 'President' as referred to D. Trump and 'Chairman' as referred to Kim J. II ? Is there any difference as far as politics is concerned ? Or is it just in context they want to use synonyms ?
The title "Chairman" refers to Jong-un's position as the chairman of the Workers' Party of Korea. In the US, the chair of the Republican National Commitee, Ronna Romney McDaniel, might be considered the current equivalent.
Kim Jong-un is also the Supreme Leader of the DPRK, which is more similar to the role of the President in the US.
To be more general, the formal title of a national leader and the power that they hold may seem to have only an arbitrary relationship; a title may derive from historical roots dating back to a different political structure, for example.
A few examples:
In the US the Mayor of a town or city may have a lot of power, or may only be carrying out decisions made by a City Manager (which is a civil servant without political power in other places.)
In countries such as the US the President has a lot of power; in Israel the Prime Minister has the political power and the President is a symbolic head of state much like the King or Queen in many Constitutional Monarchies.
in autocratic countries the Chair of the party in power may be the ultimate source of power, but in the US the Chairs of the major political parties are generally relatively unimportant except for political fundraising efforts. (I am wildly simplifying matters here, but the point is that the same title is used for two very different rules.)
The word "Secretary" is used for many different political purposes.