Just to add to Lutz's comment. There are generally three different technologies running on 12V dc and 230Vac sold as "coolers"
The compressor type mentioned by Lutz, is undoubtedly the best as it uses the same compressor technology used by your domestic fridge and freezer. If its designed for 12Vdc you would need as suitable 230v ac to 12Vdc converter to use it.
The second technology uses the Absorption principle and this is the common technology used in caravan fridges. In addition to the electrical supply options they often als include the ability to run on gas as well, hence their suitability for caravan and camping. However they are not as efficient as the compressor type coolers, and they do tend to have less cooling capacity in hot weather.
These are usually prewired to run from 12Vdc and 230Vac and gas or gas cartridges
The last common technology is thermoelectric cooling which uses the Peltier effect units. These have become very popular as the coolers can also be run as warmers BUT and its a big BUT , they are very inefficient and generally only really capable of cooling by about 15C above or below ambient and they can't move a large amount of heat, this means it takes ages to cool something down, so its best to consider them for use with pre chilled/ warmed items. These are almost always designed for 12V but some come with a suitable 230Vac to 12Vdc converter
In general compressor coolers are best but probably most expensive,
Multi fuel absorption coolers are next best and are also quite costly
Thermoelectric Peltier coolers are cheapest but least effective