Yes, he means PSU. If you have a weaker one then the 5670 is the card for you. The 9800GT takes slightly more power. (unless you get one of the green ones.) The 9800GT is the better performer, while the 5670 supports DX11. You'd probably be happy with either one.
Lite-On is an ok brand so even if the 9800GT is the standard version it can likely handle the card.
The 9800GT comes in two different versions. There is the regular version with a 6-pin power connector and a lower power version that drops the power connector and is underclocked from 600mhz to 550mhz. The performance of the low power version and the HD5670 is very similar while the regular 9800GT should be about 10% faster than either. The HD5670 has some advantages though. It is DX11 compatible which is a nice feature to have, supports 3 monitors and has more advanced audio/video playback features for home theater use.
What card you should get depends on the native resolution of your monitor so we need to know that before we can make a real suggestion. The cards you are looking at now are generally appropriate for low resolutions and will do an ok job at 1280x1024 and below. The will probably even be able to handle Crysis 2 at those resolutions although perhaps not on high settings or with anti aliasing.
If your resolution is higher than that you will want a better card. Basically it goes something like this:
decent = HD5670/9800GT
good = HD5750/HD4850/HD4770/GTS 250
great = HD5770/HD4870/GTX 260
decent = HD5750/HD4850/HD4770/GTS 250
good = HD5770/HD4870/GTX 260
great = HD5830/HD4890/GTX 275
decent = HD5770/HD4870/GTX 260
good = HD5830/HD4890/GTX 275
great = HD5850/GTX 470
the best = HD5870/GTX 480/HD5970
The two best values for the money right now in general imo are the HD5770 and HD5850. They are well priced, power efficient and DX11 compatible. The HD5770 will likely be ok on your current power supply but I would need to know the model number or the listed amperage on the +12v rail(s) to tell you for sure.
The main difference between cards will be the cooler, warranty and price.
The GTS 250 is questionable on your current power supply. The cards I listed that will likely work without needing a new one are the HD5670/HD5750/HD5770/HD4770/9800GT.