And to compliment saltedeggman's excellent answer, real server also sports more expensive and reliable hardware.
Such as Athlon Opteron or Intel Xeon processor, that is designed with reliability in mind (with price to boot)
SCSI hard drives (that are designed to provide at least three years of 24x7 service on a controlled environment -> air conditioned)
Certain brand optical drives that are very common to ensure maximum compatibility with the server operating system that it is running
Server operating systems such as Windows Server, SQL Server, Linux Enterprise Server, Netware, etc...
These are way different that regular PCs, but we are seeing more and more of server hardware being taken up by enthusiast to fit in their PCs