(1) See 
computer on a stick.
(2) A desktop computer in a small case that takes up very little desk space.  There are numerous Windows mini PCs, and the Mac comes in a mini model as well.  Configurable with the same CPUs and capacities as full-size desktop computers, a mini PC has no internal expansion, much like an all-in-one computer where all components are housed inside the monitor case.  See 
Mac mini, 
NUC and 
all-in-one.
Desktop Mini PC
Taking hardly any desk space and loaded with ports for connecting peripherals, these AOpen mini PCs are equipped with a CD/DVD drive, hard disk and Intel CPU from Pentium to i7.  (Images courtesy of AOpen Inc.)