Fan Coil Unit (FCU) is like a split unit, where the chilled water pipe comes in the room , gets circulated through the coil in the unit cooling the air circulated by the fan in the FCU. The FCU is just the portion which is insatlled inside the room and rest of the HVAC system is outside .
Air Handling Unit (AHU) is bigger than FCU and is installed above slab level and the chilled water coil and fan is inside the AHU . It directly transfers air through ducting and diffusers to the Air conditioned area. In this case air ducting comes to area instead of chilled water piping.
FCUs are used for compactness and flexibilty of operation and save fan power in contrary to much bigger AHUs.