The Dem map makes sense, Cordray did best in Central and western Ohio, where there is a low amount of Trumpiness, meanwhile Schiavoni/Kucinich were strongest in the industrial/Ohio River areas.
Maybe this explains the results for Kucinich, though the fact that Kucinich was mayor of Cleveland and Representative from a district in Cuyahoga was probably just as important (which makes his performance there really abysmal). On the other hand Schiavoni was a state Senator with a district composed of Mahoning and Columbiana. Cordray also did worse in the Ohio river valley because the fourth placed candidate, Bill O'Neill, achieved his best results in the southwestern corner of the state, despite him being once an appellate judge from northwestern Ohio (and his running mate is also from this region).
I have no idea how to interpret the Rep gubernatorial primary map. The assortment of counties won by Taylor have no obvious connection. The only thing I can think of is that DeWine has been in office for enough years that those counties are places with some miscellaneous grievance with something he or his office has done.
On the other hand, Taylor is from Summit county and was a member of the Ohio House with a district in that county, yet did no better there than her average performance in Ohio.