One is integrated into the motherboard and the other is a dedicated card which would be somewhat better then the onboard graphics but depending on what you would be doing with your computer, you may need a better card.
If you aren't doing any gaming then the onboard graphics will work, if you'll be doing any gaming, I would highly recommend getting a different card.
Rage? Intel 82845G*? I'm assuming that you're going to be doing no gaming or anything that requires any form of hardware-accelerated graphics, so really the only thing that matters is whether they support high enough resolutions for your monitor. Which, I'm guessing, the Intel won't, IIRC those things have a max resolution of 1024x768 and I've no idea what 22" HD monitor would have that as its native resolution... though to be frank, I have my doubts about the Rage as well (though I know for a fact that it goes a lots higher than the Intel IGP).
How old is this machine you're talking about? Are you actually planning on buying it or is it one you already have and want to upgrade? What do you use it for?
Rage? Intel 82845G*? I'm assuming that you're going to be doing no gaming or anything that requires any form of hardware-accelerated graphics, so really the only thing that matters is whether they support high enough resolutions for your monitor. Which, I'm guessing, the Intel won't, IIRC those things have a max resolution of 1024x768 and I've no idea what 22" HD monitor would have that as its native resolution... though to be frank, I have my doubts about the Rage as well (though I know for a fact that it goes a lots higher than the Intel IGP).
How old is this machine you're talking about? Are you actually planning on buying it or is it one you already have and want to upgrade? What do you use it for?