So I have Nike-DOS 3.42/1.21 (1988/1989) and Kiev-DOS 4.01/2.07 (1990). When viewing them in code they don't look anything alike. Nike-DOS has a lot of extra internal commands, while Kiev-DOS even has viewer commands than standard MSX-DOS. And yet, they share some similarities.
First of all they both have a SET command. SET A will switch to 80 columns mode, SET B will switch to 40 columns mode. Other SET commands seem to have no effect. But why? Nike-DOS also has the regular MODE command, while Kiev-DOS hasn't.
Second, if you enter a non-existing command, let's say MRC they respond similarly. Nike-DOS will respond '? MRC', Kiev-DOS will respond 'MRC?'. Both instead of the regular 'Bad command or file name' error from MSX-DOS.
And of course they probably share a Ukrainian origin. On Helger Lipmaa's page he tells Ted Chary was called Alex Garmash in real life and he lived in Kharkov, Ukraine. I don't have any backstory for Kiev-DOS, except of course Kiev is located in Ukraine as well.
Who knows the relation (if any) between these MSX-DOS clones? Who knows about other versions of these? According to the forum, there were multiple versions of Nike-DOS. Is Kiev-DOS one of them?