Zemstvo comes from the word zemlya, meaning land. When they were imposed in 1864, representation was based upon land ownership, meaning large private landowners had a lot of individual power, peasant communes had limited collective power. They administered provinces, but an equivalent was used to administer town at a later date.
Soviet means council. They were based in cities, but similar institutions in the countryside popped up in 1917 too. The primary members were either soldiers or striking factory workers. Revolutionaries held power, unlike the zemstvo where the aristocracy and liberal politicians held power.