Translation:Kateřina lives in Bohemia and Žofie in Moravia.
It is just like that. Some geographical places use "v", some "na". This usage can change in time and can differ between the standard language and common vernacular. It can differ between locals and speakers from other areas. There is no other way than learn each individually.
Note that an older variant was: "Dějiny národu českého v Čechách a v Moravě" (The history of the Czech nation in Bohemia and in Moravia)
"V" is much more common among different geographical names, so it is usually the safer bet.
"Na" for certain countries: na Slovensku, na Ukrajině, na Rusi (=the old Rus', Ruthenia),
"Na" for certain cities and towns: na Kladně, na Mělníce
various quarters of Prague: na Malé Straně, na Starém Městě (pražském), na Klárově, na Vinohradech, na Žižkově, na Karlově, na Vyšehradě, na Pankráci,... but v Libni, v Holešovicích, ve Strašnicích, v Košířích, v Troji (notice that some of those with "na" are located in or near the centre)
The relevant article (in Czech) http://prirucka.ujc.cas.cz/?id=640