There are 9 Shinkansen lines in Japan. 9 lines include 7 full standard Shinkansen and 2 mini Shinkansen. One of the differences between full standard and mini is that only Shinkansen trains run on full standard lines but ordinary trains also run on mini Shinkansen lines. These two mini Shinkansen lines are Akita and Yamagata Shinkansen, which officially run on Tazawako line and Ou main line.
Ordinary JR lines' gauge is narrow-gauge railway, 1067 mm but full standard Shinkansen is standard-gauge railway, 1435 mm. Therefore it is physically impossible for Shinkansen trains to run on ordinary JR lines. Tazawako line and Ou main line(between Fukushima and Shinjo stations) were narrow gauge but converted to standard gauge to run the mini Shinkansen trains.
The big difference between full standard and mini is the speed. Cruise speed of full standard Shinkansen is more than 240 km/h, the maximum is 320 km/h on Tohoku Shinkansen but maximum speed of mini Shinkansen is 130 km/h, which is similar to ordinary limited express trains.
However, mini Shinkansen trains can run on full standard Shinkansen lines, which means that the maximum speed can be 320 km/h on Tohoku Shinkansen lines between Tokyo and Akita/Fukushima.