What is the difference between the fan coil unit and hide away unit? 

I think here hideaway unit refers to Hideaway Horizontal Fan Coil Units, it is one type of fan coil units. 

From the shape or the outlooking of the the fan coil units, normally we have below different divisions for fan coil units: 
four way cassette fan coil units; 
one way cassette fan coil units; 
high wall mounted fan coil units; 
Hideaway Horizontal Fan Coil Units,also called ceiling concealed ducted type fan coil units. 
vertical free stand fan coil units; 
ceiling floor fan coil units; 
high static pressure fan coil units, it is also hideaway in the ceiling, the difference betwwen high static pressure fan coil units and Hideaway Horizontal Fan Coil Units is that, the static pressure are different. 
For more info i think you can check it at: 
http://www.china-fancoil.com/products.ht... 
And below picture shown the different types of fan coil units.