There is often some confusion with the names of engineering products and this applies to heat exchangers and air coolers just like any other product. The confusion comes from the literal apportioning of a products purpose to its name.
“Air to Air cooler” is a classic example.
In the industry, the product may simply be referred to as a “charge air cooler” or even just an “air cooler”. Because the product uses air to cool the air, lay people are inclined to add the word “air” to the name.
To be clear, the traditional engine mounted charge air coolers manufactured by Vestas aircoil use cool water, passed inside tubes to cool hot air that is flowing on the outside of those tubes. Thus, we are exchanging heat between the hot air and the cool water – a “heat exchanger”.
An “air to air” cooler is likely to be much larger in size and may be situated remotely from the engine. Often referred to as a “dry cooler“.
Vestas will advise you about which option is best for your circumstances and design accordingly.
Go to what is a charge air cooler for more detail.