Air conditioning system is the system which keeps on control and maintains the particular condition (that is required temperature and humidity of air) in the closed space.
It is technically defined as a system which controls temperature, humidity, purity and motion of air to produce desired effects upon the occupants of the space. In case of air cooler, which has the capability to cool the air inside the space does not maintain particular temperature and humidity of the air. In response to atmospheric seasons we can have winter, or summer air-conditioning system, but any air cooler will not do so.
A so-called air cooler or desert cooler is basically a humidifier (Humidity is the moisture or water content of air). An “air-cooler” mixes water vapour with air by means of a rolling pad of moist cloths of fibre, and makes the air seem cool, but actually more humid (high moisture content).
An Air conditioner/refrigerator, basically a dehumidifier, works as follows:
A fluorocarbon refrigerant gas (such as “a Freon”) is compressed. On compression it is pressurized and heated. The extra heat is removed by air (from a fan) or by cooling water as in the case of large (Central A/c) units. 
The high-pressure refrigerant is expanded. In contrast to heating on compression the refrigerant, on expansion by sudden reduction in pressure, becomes very cold due to Joule Thomson effect.
By heat exchange with the very cold refrigerant (which has now become liquid) passing through tubes (that have fins for good heat exchange) the air paning ore, becomes cold and is circulated in the space (room etc) to be cooled. Because the air is cooled considerably, extra moisture content on humid days may be seen dripping from the air conditioner.
For efficient operation the room in which an air conditioner is used will have to have its doors & windows closed. On the other hand, when direct cooler are in use, at least one window should be kept open as otherwise the humidity will become very uncomfortable.
P.S.: When humidity in the atmosphere is more, curcating will be more as the sweat will not dry fast enough. In contrast, when humidity is very less as in very cold days when all the moisture in the air would have condensed leaving the atmospheric air “dry”, lips and body skin may be seen getting cracks.