If you take a look at air-cooled engines, you will see that many use extra fins to draw the heat away from the engine where the air can pass over the fins and help cool the engine. Most air-cooled engines are not HIGH HORSEPOWER engines compared to water cooled engines.
Water cooled (or liquid cooled) engines use a fluid (water) to draw the heat from the engine and deliver that heat to an area where the air can cool the liquid down. So technically, all engines are air cooled, with some using a liquid to transfer the heat to the air, and others using metal to transfer the heat to the air. CASE SOLVED.
But the construction of the air cooled and water cooled engines differ. The air cooled are made with thin material to make it easier for the heat to be removed from the engine, while the water cooled are made thicker and heavier to support the liquids inside PLUS all the passages needed to remove that heat from the engine to go someplace where the heat can be removed.
And some water cooled engines need to be extra thick in material to produce the horsepower/torque needed. Look at a diesel engine. With 15 to 1 compression ratio, they need the heavy cast iron to keep from exploding. Not a lot of horsepower, but the torque can rip your arm off.