as part of the large area airconditioning component, the cooling tower is where heat is exchanged. it's usually located outside, in an area where acoustics wouldnt be a problem (like rooftops or behind a building). u will notice huge fans operating inside the cooling towers, and sometimes u can even see water cascading down cooling the air for the primary intakes.

AHU on the other hand is the horizontal distribution mechanical room for a floor. this is where cooled air from the plant room (usually located in the basement) is distributed for a particular floor. so in a highrise building, it will have at least one AHU for each floor.

both are not feasible for normal houses or small buildings as it's too expensive. i would recommend just using a split unit.

AHU stands for air handling unit. basically it's a pump room that distributes cooled air from the plant room to each floor. plant room is not efficient enough to send cool air to every part of the building. so it will be sent to AHUs as main distribution points for each floor.

there will be ducting coming out of the AHU running through the ceiling (or under the floor), normally covered in silver/aluminium foils. u can see this if u open up the false ceiling in office buildings or even retail shops in shopping complexes that bares their ceilings.

so the AHU doesnt do anything to cool the building. it's just a distributor. in winter, it can be used to handle warm air as well.

well, i hardly got involved with AHUs directly either. as an architect we have to know how each and every thing works, including how to place AHUs and how to get the best effects .