Answer:
Well, you have rocket engines and jet engines which aren't internal combustion engines, and various types of internal combustion (Otto cycle -- what you probably have in most cars, Diesel cycle like small diesel cars and trucks, Wankel cycle like in Mazda rotary engines like the RX series, and 2-stroke like in dirt bikes and lawnmowers). There are also Stirling engines which work on heat differential but don't make a lot of power and are usually quite tiny and for demonstration or cooling purposes.
So yes, internal combustion engines are a type of engine.