I am a non-engineer and I am using a gas power plant data base. Some plants listed are of the type "combustion engine", some of the type "gas turbine", some "steam turbine" and some "combined cycle". I believe to understand that combined cycle is a combination of combustion engine and steam turbine. But what is the difference between combustion engine and gas turbine then? Or does it mean the same?
Combustion engine - an internal combustion engine like a car motor, with pistons moved in cycles. It's inefficient but can be easily scaled down to almost arbitrarily small sizes; usually used as a backup.
Gas turbine - in power plants, these are very similar in construction to jet engines, where gas is the fuel - a multi-stage turbine compressor, a turbine on exhaust, high RPM; the torque produced is used to run the generator. It's not as efficient as steam or combined cycle, though more than combustion engine - but the power output can be rapidly tuned to needs, providing a response to changing demand (which is typical for the "more inert" types that use steam.)
Steam turbine - gas heats water in a boiler; overheated steam runs through turbines, then is cooled. This is the same principle as great most other thermal power plants (coal, nuclear, geothermal). It's usually a large installation and may take hours to get up to speed (so no rapid response to demand + waste of energy as demand rapidly vanishes) but it has a very good efficiency.
Combined cycle - exhaust from gas turbine (the "jet engine") is used to heat water into steam and run a steam turbine. Better efficiency than both above, and provides the much desired rapid response. Of course cost of construction is similar to sum of costs of construction of the two, and maintenance is more complex, but the operational costs are reduced.