Is there a difference between a nuclear power plant and a hydroelectric power plant?

Of course there is a difference.

Nuclear power plant: Firstly, a nuclear reaction occurs in the nuclear reactor, which generates huge heat, turns water into steam with high temperature and high pressure, drives the turbine to rotate and drives the generator to produce electricity. ---Conversion of nuclear energy into electrical energy

Hydroelectric power plant: Water falling from a height has kinetic energy, which turns the blades of the turbine, driving the generator to produce electricity.

－－－－Convert water energy (mechanical energy) into electrical energy.