The river bank is more closely the physical edge of the river: at the river bank there are perhaps grass, reeds, or stones.
The riverside is a wider concept: at the riverside there may be shops, restaurants, or a park, which look over the river.
I was raised in the city of Riverside; so-called because the city is situated along the Santa Ana river. The bank is the immediate land that separates the water from the rest of the land. Riverside is an area that stretches alongside a river, which can include the riverbank/bank, too. Riverbank and bank mean the same to me.
