Since Ancient Age until Early Modern Age, Japan had been divided into over
60 countries. The countries had been the formal-administrative district,
then we may call them provinces. May be called small kingdoms which were
to be governed by the count-class or duke-class lords.
For examples of such Provinces, we may remember Yamato, Musashi, Omi, Mino, Shinano, Owari, Suruga, Satsuma or so.
In the Edo Period each coutry was devided into 3 - 5 counties or duchies
which were administrated by Lords (counts, earl or dukes). But some lords fief reached beyond the country (province) borders.
Counties or duchies were the military-political units which was relatively
independent each other and from the Tokugawa Shogunate government. However the Shogunate government could re-allocate lords when they failed to govern their fief peacefully.
In Kanji-description Shinano is represented as 信濃, then we call Shinano country
Shin-shu（信州）. In a geographic sense, Shin=信 is the simplified transcription of
Shinano and shu=州 means the country, the province or the states of federal-system
like U. S. A..
Likewise, Kai （甲斐） is transcribed Ko-shu （甲州）.