Main bases of hydro-turbines types

In addition to what you rightly said, hydro turbines can be classified based on how water flows through the turbine itself. When passed through a turbine, water can take a variety of different paths. This leads to three categories of water flow through turbines:[2]

In impulse turbines, the pressure of the liquid doesn't change in the turbine itself. Instead, pressure changes occur only in the nozzles that direct water flows to the turbine, while the turbine itself operates at atmospheric pressure. These turbines are composed of a jet nozzle or series of nozzles that direct water to the blades of a turbine. Multiple nozzles are usually used where a large wheel isn't feasible. When the water strikes the blades (designed specially to reduce drag), it changes velocity. This leads to a change in momentum, exerting a force on the turbine blades. These turbines rely on the ability to take all kinetic energy from the water to have high efficiencies. Unlike reaction turbines, impulse turbines do not need to be submerged. Types of impulse turbines include Pelton turbines, Turgo turbines, and Crossflow turbines. For more information on where these turbines are used and how they are constructed, follow the links to their respective pages.

In reaction turbines, the pressure of the water changes as it moves through the blades of the turbine. Unlike an impulse turbine, the reaction turbine directly uses water pressure to move blades instead of relying on the conversion of water pressure to kinetic energy. This means that reaction turbines need to be submersed in water. Additionally, components of these turbines must be able to handle high-pressure levels inside the turbine. Here, the fluid velocity and reduction in water pressure cause a reaction on the turbine blades, moving them. Types of reaction turbines include Kaplan turbines and Francis turbines. For more information on where these turbines are used and how they are constructed, follow the links to their respective pages.

Regards