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Dear Hassan,
The Sharif's answer is correct. But let me to add some more:
1- Fan coils are split units installed in rooms when the AHU is a centralized unit installed in mechanical rooms or roofs.
2- Fan coils are mainly designed considering no fresh air, when fresh air is considered mainly in AHUs.
3- The coils (fin-plate heat exchangers) used in fan coil units are generally one common coil used for both cooling and heating functions. But because of high capacity of AHUs, separate coils (fin-plate heat exchangers) are considered for cooling and heating functions.
4- The fans in FCUs are commonly direct drive, when it is belt driven (generally) in AHUs.
5- When we install AHU, we must consider ductwork too. But when we use fan coils, just in ducted fan coils (not wall mounted/room fan coils) duct work is considered.
6- Depends on philosophy of controlling air conditions, You have much more control on temperature of different zones by Fan coils without controlling on humidity and air quality. When in AHUs you (generally) cannot reach proper control in different zones separately, but by considering additional accessories such as humidifires, filters,... you will have better control on humidity and air quality.
Regards
Fan coil unit (FCU)
Fan coil units are more economical to install than ducted or central heating systems with air handling units. However, they can be noisy.
Air handling unit (AHU), is a device used to regulate and circulate air as part of a heating, ventilating, and air-conditioning system. An air handler is usually a large metal box containing a blower, heating or cooling elements, filter racks or chambers, sound attenuators, and damper Air handlers usually connect to a ductwork ventilation system that distributes the conditioned air through the building and returns it to the AHU.
the basic difference is the cooling capacity. AHU have more cooling capacity than FCU.
AHU can be equipped by another features like humidifier or dehumidifier, extra filters.