Kingdom, duchy, county, etc. can often be thought of as simply land divisions of varying sizes (though with no fixed sizes for any of them). Sometimes a piece of land was a duchy (or county, etc.) because the ruler was a duke (or count, etc.) and sometimes it was the other way around and the ruler was a duke because the piece of land he held was a duchy. A lot of tradition is bound up in the titles of various rulers and names of various pieces of land.

The grand duchy was somewhat of a latecomer to the land divisions and was created essentially to make a particularly large piece of land stand out (or, the other way around, a particularly powerful individual took the title of Grand Duke so they had more perceived authority than normal dukes).

All this applies, more-or-less, to sovereign individuals as well. Depending on tradition, level of power, etc. a sovereign could be a king, prince, (arch)/(grand) duke, etc. There is essentially no difference between a king and a grand duke within their own lands but a sovereign duke would be regarded as subordinate to a king in the wider world (and likely had less real power).