To elaborate a little bit on the difference between "Media Center Extenders" and Media Players or Bridges.
The former requires a specific operating system in order to operate and is usually made to be an accessory to an HTPC. The specific OS's are XP MCE and Vista Home Premium or Vista Ultimate. This is not too much of an issue now as pretty much everyone who is getting Vista (I think) is getting at least Home Premium - therefore they can use the extender. But this was an issue in the past - how many people bought a PC two years ago with XP MCE rather than XP Home or Pro?
The extenders also use Terminal Services - essentially they are acting as a "dumbed-down" remote desktop client from the MCE which is acting as a remote desktop server.
The media players or bridges did not require a specific OS - in fact they theoretically could be used in conjunction with Apple or Linux PCs, not just Windows PCs. These devices were seen as a "bridge" between the media content on your LAN (photos, music and video files) and your Home Theatre without any prerequisites. The forerunner of these devices was a music-only device called the Turtle Beach AudioTron that come out somewhere around 2000-2001 and allowed you to play music files from your LAN such as MP3s or WAVs. It did not require a TV - it had an LED screen for you to see what song you were selecting.
A few years later around 2003 companies like Go Video (D2730), Gateway (ADS 220), D-Link (320), HP (Digital Media Receiver ew5000), Linksys (WMB54G) etc. introduced products that were able to play music files (MP3, WAV, WMA, etc.), video files (MPG, AVI, .TS,etc.) and photos on your home theatre. The media was served up by software running on your PC or uPnP. You generally did not require a special HTPC OS.
One huge difference is that if you don't have the right OS it isn't easy to switch to using a Media Center Extender. If you were running XP Home or Pro you would have to buy MCE and reinstall your OS. With Vista if you are running Home Basic you have to buy an upgrade which is a bit easier as you can do Windows Anytime upgrade but still more expensive and not seemless.
Another huge difference is that extenders were made to seemlessly share live and recorded TV. They not only allow you to timeshift, they allow you to placeshift as long as that place is within an ethernet cable or your WiFi network. That was not the case with the media players and it is a huge benefit. If you only have one digital cable box and it is in your media room you could still watch live digital cable in your bedroom via an extender - as long as someone in the media room didn't want to watch a different show (unless you had two tuners in your MCE box). You would also have full PVR functionality - pause liveTV, start watching a 30 minute show 15 minutes in, etc. And you could schedule recordings from the extender.