Audio files are stored on a hard disk. You have two options to access them:
A PC has the audio files stored on a local HD and/or on a server somewhere in your home network.
A streaming audio player in general doesn't have a HD. It gets it music from a server. You connect to a server by providing its IP-address, browse its contents and choose a song.
Pretty much the same way as you surf the internet using your browser.
To play your own music using a streaming audio player:
After configuring everything correctly, the media player can access your collection over the home network.
A bit more complex compared with a PC.
If you want to give it a try and you have a PC running Vista or XP and a media player you can enable the media sharing and connect a media player.
If you have 2 PCs, enable media sharing and they can both play the content on the other (Vista, XP can only act as a server)
There are more differences.
Sound quality
In both cases the sound quality is as good as the on board audio allows.
In both cases you can use an external DAC to improve on it.
Streaming audio players often have a SPDIF (digital out) over coax or Toslink.
PC in general don’t offer SPDIF but USB.
Power consumption
Well designed NAS and a media players use less power than a PC.
A lightweight NAS might consume 15 Watt, a Squeezebox probably 5 Watt, a laptop probably 60 Watt
A typical audiophile worry is whether audio over the network will ever sound right.
Small wonder, if you pay Stealth Audio Cables $6,500.00 for a 1 m RCA interconnect to connect your CD player to your amp, you can't believe that sending audio over a CAT5 ( $50,00 for 100 meter) or over WiFi can sound right.
The answer is simple, you don't send audio over the network, you transfer data from one device to another. Networks are build to do bit perfect data transmission.
What is sold as “music server” is in general a dedicated computer.
Most of them are not servers properly as you can control them directly.
But a lot of them can be used as a server as well.
They have the look and feel of traditional audio equipment. In fact some companies stress that it is NOT a computer. They probably think they fence people of by calling it what is, a computer. More can be found here